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a2+b2+2ab

Posted by Riya Kumari 6 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Sunny Kumar 6 years, 5 months ago

(a+b)2

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2 x = 304142 (12 30-100 40)45

Posted by Rakesh Kumar 6 years, 5 months ago

CBSE > Class 09 > Mathematics

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a+b+c=5 and ab+bc+ac=10, then orove that a^3+b^3+c^3-3abc=-25..

Posted by Neha Krishnan 6 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

As we know,

{tex}a ^ { 3 } + b ^ { 3 } + c ^ { 3 } - 3 a b c ={/tex}{tex}( a + b + c ) \left( a ^ { 2 } + b ^ { 2 } + c ^ { 2 } - a b - b c - c a \right){/tex}

{tex}= ( a + b + c ) \left[ a ^ { 2 } + b ^ { 2 } + c ^ { 2 } - ( a b + b c + c a ) \right]{/tex}

{tex}= 5 \left\{ a ^ { 2 } + b ^ { 2 } + c ^ { 2 } - ( a b + b c + c a ) \right\}{/tex}

{tex}= 5 \left( a ^ { 2 } + b ^ { 2 } + c ^ { 2 } - 10 \right){/tex}

Now, {tex} a + b + c = 5{/tex}

Squaring both sides, we get

{tex}( a + b + c ) ^ { 2 } = 5 ^ { 2 }{/tex}

{tex}\Rightarrow a ^ { 2 } + b ^ { 2 } + c ^ { 2 } + 2 ( a b + b c + c a ) = 25{/tex}

{tex}\therefore a ^ { 2 } + b ^ { 2 } + c ^ { 2 } + 2 ( 10 ) = 25{/tex}

{tex}\Rightarrow a ^ { 2 } + b ^ { 2 } + c ^ { 2 } = 25 - 20 = 5{/tex}

Now, {tex}a ^ {3} + b ^ {3} + c ^ { 3 } - 3 a b c = 5 \left( a ^ { 2 } + b ^ { 2 } + c ^ { 2 } - 10 \right){/tex}

{tex}= 5 ( 5 - 10 ) = 5 ( - 5 ) = - 25{/tex}

Hence, proved.

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The sum of rational number is always rational? Please comment the answer...

Posted by Tanushka Rawat 6 years, 5 months ago

CBSE > Class 09 > Mathematics

4 answers

Sunny Kumar 6 years, 5 months ago

Yes 2+2=4 it will always be a rational no

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Nikita Virmani 6 years, 5 months ago

Yes The sum of rational is always rational

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Ayan Ali 6 years, 5 months ago

Yes always be rational no.

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M M 6 years, 5 months ago

yes

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If a+b+c=9 and a²+b² +c²=35,find the value of a³+b³+c³-3abc

Posted by Pradum Dubey 6 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Ishika Darpe 6 years, 5 months ago

a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)

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Ex 13.7

Posted by Dayaram Yadav 6 years, 5 months ago

CBSE > Class 09 > Mathematics

0 answers

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Different identities

Posted by Green Tea 6 years, 5 months ago

CBSE > Class 09 > Mathematics

0 answers

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A= Set of all even positive integers less than 9

Posted by Keimah Thingtlang Naupangfela 6 years, 5 months ago

CBSE > Class 09 > Mathematics

0 answers

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Examine wheather √2 is rational or irrational number

Posted by Harsh Patel 6 years, 5 months ago

CBSE > Class 09 > Mathematics

2 answers

Sunny Kumar 6 years, 5 months ago

Root 2 is an irrational

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Srishtika Murugan 6 years, 5 months ago

Root 2 is an irrational no.

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4root 3/2-root 2-30/4root 3-3root 2-3root 2/3+2root 3

Posted by Rima Tiwary 6 years, 5 months ago

CBSE > Class 09 > Mathematics

0 answers

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Find a rational number between -2 by 3and 1by 4 ,

Posted by Sunil Harjai 6 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

The rational number {tex}\left(\frac{-2}{3}+\frac{1}{4}\right){/tex}{tex}\div{/tex} 2 lies in the middle of the two given rational numbers, that is, {tex}\frac{-2}{3}{/tex} and {tex}\frac{1}{4}{/tex}.
Now, {tex}\left(\frac{-2}{3}+\frac{1}{4}\right){/tex} = {tex}\frac{(-2) \times 4 + 3 \times 1}{12}{/tex} = {tex}\frac{-8+3}{12}{/tex} = {tex}\frac{-5}{12}{/tex}
{tex}\therefore{/tex} {tex}\left(\frac{-2}{3}+\frac{1}{4}\right){/tex} {tex}\div{/tex} 2 = {tex}\frac{-5}{12}{/tex} {tex}\div{/tex} 2 = {tex}\frac{-5}{12}{/tex} {tex}\times{/tex} {tex}\frac{1}{2}{/tex} = {tex}\frac{-5}{24}{/tex}
Thus, the required rational number is {tex}\frac{-5}{24}{/tex}. That is, {tex}\frac{-2}{3}{/tex} < {tex}\frac{-5}{24}{/tex} < {tex}\frac{1}{4}{/tex}.

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5×x=16. So find the value of 5×x÷2+1

Posted by Sagar Gupta 6 years, 5 months ago

CBSE > Class 09 > Mathematics

2 answers

Railway Hub 6 years, 5 months ago

3Thank You

Sagar Gupta 6 years, 5 months ago

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√x+1/x find value , if x = 7+√40

Posted by Lata Singh 6 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Dipanshu Verma 6 years, 5 months ago

hiii

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4(1/2)

Posted by Bhoomi Mishra 6 years, 5 months ago

CBSE > Class 09 > Mathematics

2 answers

Aditi Mundhe 6 years, 5 months ago

4 x 1/2 4/2 =2

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Upllakshaya Jain 6 years, 5 months ago

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cube root of 2 × fourth root of 3

Posted by Sri Hari 6 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

[email protected] Yuvibala 6 years, 5 months ago

568

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Is the sss and rjs criteria of congruency

Posted by Navneet Ghuman 6 years, 5 months ago

CBSE > Class 09 > Mathematics

2 answers

Ayan Ali 6 years, 5 months ago

Yes

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Aditi Mundhe 6 years, 5 months ago

SSS and RJS are none of the criterias of congruency.

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Which identity will be use to factories y2-xby 100 2

Posted by Vrushabh Tubachi 6 years, 5 months ago

CBSE > Class 09 > Mathematics

0 answers

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6x +19x +15

Posted by Banny Sundrapalli 6 years, 5 months ago

CBSE > Class 09 > Mathematics

3 answers

Sunny Kumar 6 years, 5 months ago

6x+15x-6x+15 by(middle term split) 3x(2x-5x)-3(2x-5x) (3x-3) (2x-5x) I ? think the question is wrong because the right Question is 6x2square +9x +15

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Narendra Kumar 6 years, 5 months ago

6x+19x+15 6x+9x+10x+15 3x(2x+3)+5(2x+3) (2x+3)(3x+5)

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Ruchika Aggarwal 6 years, 5 months ago

6x^2+19x+15 6x^2+9x+10x+15 3x(2x+3)+5(2x+3) (3x+5)(2x+3)

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Define axioms and postulates

Posted by Mahi Singh 6 years, 5 months ago

CBSE > Class 09 > Mathematics

2 answers

Chirag Sharma 6 years, 5 months ago

He used the term 'POSTULATE' for the assumption that geomatry. AXIOMS are also true statement in which they are appiabale for only mathematics are called axioms.

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Manjunatha Setty K A 6 years, 5 months ago

Axioms are true statements in which they are applicable for only mathematics are called axioms Postulates are also true statements in which they are applicable for only geometry

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Expand form of (3a+4b)3

Posted by Ashmit Gardia 6 years, 5 months ago

CBSE > Class 09 > Mathematics

3 answers

Sarthak Shavarn 6 years, 5 months ago

Abe nikal yaha se

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Mahi Singh 6 years, 5 months ago

(3a)(3a)(3a) +(4b)(4b)(4b) +3(3a)(4b)(3a+4b) 27a³+64b³+108a²b+144ab²

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Yogita Ingle 6 years, 5 months ago

Using the identity (a + b)³ = a³ + b³+ 3a²b + 3ab² , we have , we have
= (3a)³ + (4b)³ + 3 (3a)²(4b) + 3(3a) (4b)²
= 27a³ + 64b³+ 108a²b + 144ab²

which is the required expanded form.

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A cylindrical tub container a radius 12cm to a depth 20cm . A spherical iron ball is drop into the tub and thus the level of water is rased by 6.75cm . What is the radius of the ball?

Posted by Sumit Karan 6 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

According to question it is given that
Radius of cylindrical tub = 12 cm
Depth of cylindrical tub = 20 cm
Let us suppose that (r) be the radius of spherical ball
Again it is given that level of water is raised by 6.75 cm
Now, according to the question,
Volume of spherical ball = Volume of water rise in cylindrical tub
{tex}\Rightarrow \quad \frac { 4 } { 3 } \pi r ^ { 3 } = \pi ( 12 ) ^ { 2 } \times 6.75{/tex}
{tex}\Rightarrow \frac { 4 } { 3 } r ^ { 2 } = 12 \times 12 \times 6. 75{/tex}
{tex}\Rightarrow \quad r ^ { 3 } = \frac { 12 \times 12 \times 6.75 \times 3 } { 4 }{/tex}
{tex}\Rightarrow \quad r ^ { 3 } = 729{/tex}
{tex}\Rightarrow \quad r = \sqrt [ 3 ] { 729 } = 9 \mathrm { cm }{/tex}
Therefore, Radius of the ball = 9 cm

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x3+3x3+3x+1÷x+

Posted by Yash Sihag 6 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Vrushabh Tubachi 6 years, 5 months ago

Using identity solve (x-3)(x+3)

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An exterior angle of a triangle is 115°& one of the interior opposite angle is 35°. Find the other two angles.

Posted by Hariom Dalal 6 years, 5 months ago

CBSE > Class 09 > Mathematics

2 answers

Sia ? 6 years, 5 months ago

Let in {tex}\bigtriangleup{/tex}ABC, exterior {tex}\angle{/tex}ACE = 115^o and {tex}\angle{/tex}A = 35^o
We know that,
{tex}\angle{/tex}ACE = {tex}\angle{/tex}A + {tex}\angle{/tex}B (Exterior Angle Theorem)
{tex}\Rightarrow{/tex} 115^o = 35^o + {tex}\angle{/tex}B
{tex}\angle{/tex}B = 115^o – 35^o = 80^o
Again, in {tex}\bigtriangleup{/tex}ABC,
{tex}\angle{/tex}A + {tex}\angle{/tex}B + {tex}\angle{/tex}C = 180^o
(The sum of the three angles of a triangle is 180^o)
{tex}\Rightarrow{/tex} 35^o + 80^o + {tex}\angle{/tex}C = 180^o
{tex}\Rightarrow{/tex} 115^o + {tex}\angle{/tex}C = 180^o
{tex}\Rightarrow{/tex} {tex}\angle{/tex}C = 180^o – 115^o = 65^o

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Srishtika Murugan 6 years, 5 months ago

In the figure, By linear pair axiom, Angle ACB = 180 - 115 =65 By angle sum property, Angle ABC=180-(AngleBAC +AngleACB)=180-(35+65)=180-100=80

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Cos10+cos20+....+cos170=

Posted by Balamourougane Balamourougane 6 years, 5 months ago

CBSE > Class 09 > Mathematics

0 answers

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Prove that root 2 or √2 is irrational no.

Posted by Uttpan Patnaik 6 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

Suppose {tex}\sqrt2{/tex} is a rational number. That is , {tex}\sqrt2{/tex} = {tex}\frac{p}{q}{/tex} for some p{tex}\in{/tex}Z and q {tex}\in{/tex}Z. We can assume the fraction is in lowest fraction, That is p and q shares no common factors.

Then {tex}\sqrt2q=p{/tex}

Squaring both side we get,

{tex}2q^2=p^2{/tex}

So {tex}p^2{/tex} is a multiple of 2,

let's assume {tex}p=2m{/tex}

Then, {tex}2q^2=\left(2m\right)^2{/tex}

{tex}2q^2=4m^2{/tex}
Or {tex}q^2=2m^2{/tex}
So {tex}q^2{/tex} is a multiple of 2,
{tex}\therefore{/tex} q is multiple of 2
Thus p and q shares a common factor.This is contradiction.
{tex}\Rightarrow {/tex}{tex}\sqrt { 2 }{/tex} is an irrational number.

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Number of sides in two regular polygon are in the ratio 5:4 and differnt between their interior angle 156 find the no. Of sides in two polygon.

Posted by Yuvika Garg 6 years, 5 months ago

CBSE > Class 09 > Mathematics