CBSE > Class 10 > Mathematics | CBSE Board | Homework Help

In equilateral {tex}\triangle{/tex}ABC. 4BD = BC
Construction: Draw AE {tex}\perp{/tex} BC. {tex}\therefore{/tex} BE = {tex}\frac{1}{2}{/tex}BC.
In right {tex}\triangle{/tex}AED, AD² = DE² + AE²{tex}\Rightarrow{/tex} AE² = AD² - DE² ..(i)
In right {tex}\triangle{/tex}AEB, AB² = AE² + BE² {tex}\Rightarrow{/tex} AB² = AD² - DE² + BE² [using (i)]

{tex}\Rightarrow{/tex} AB² + DE² - BE² = AD²
{tex}\Rightarrow{/tex} AB² + (BE - BD)² - BE² = AD²
{tex}\Rightarrow{/tex} AB² + BE² + BD² - 2BE.BD - BE² = AD²
{tex}\Rightarrow{/tex} AB² + ({tex}\frac{1}{2}{/tex}BC)² - {tex}2 \times \frac{1}{2}{/tex}BC{tex}\times \frac{1}{4}{/tex}BC = AD²
{tex}\Rightarrow{/tex} AB² + {tex}\frac{1}{16}{/tex}BC² - {tex}\frac{1}{4}{/tex}BC² = AD²
{tex}\Rightarrow{/tex} BC² - {tex}\frac{3}{16}{/tex}BC² = AD²[{tex}\because{/tex} AB = BC]
{tex}\Rightarrow{/tex} {tex}\frac { 13 \mathrm { BC } ^ { 2 } } { 16 }{/tex} = AD²
{tex}\Rightarrow{/tex} 13BC² = 16AD²

0Thank You

ANSWER

Prove that √2 is irrational number?

Posted by Ꭾꮢꮛꮛꮦ Ꭾꭷꮢꮗꮧꮭ 6 years, 5 months ago

CBSE > Class 10 > Mathematics

4 answers

Krishan Kumar Saini 6 years, 5 months ago

Prove that 0 is a irrational

0Thank You

Yogita Ingle 6 years, 5 months ago

Let us assume √2 is rational number.
a rational number can be written into he form of p/q
√2=p/q
p=√2q
Squaring on both sides
p²=2q²__________(1)
.·.2 divides p² then 2 also divides p
.·.p is an even number
Let p=2a (definition of even number,'a' is positive integer)
Put p=2a in eq (1)
p²=2q²
(2a)²=2q²
4a²=2q²
q²=2a²
.·.2 divides q² then 2 also divides q
Both p and q have 2 as common factor.
But this contradicts the fact that p and q are co primes or integers.
Our supposition is false
.·.√2 is an irrational number.

1Thank You

Niveditha C S 6 years, 5 months ago

Proof:let us assume √2 is an rational number. Therfore,√2=p/q where p and q are coprime and q is not equal to 0 P= √2q Squaring on both sides, (P)square=(√2)square Psquare=2square Therefore,qsquare =psquare/2 Psquare is divisible by 2 P is also divisible by 2. {Equation 1} Let p=2k where k is some constant √2q=2k Squaring on both sides, √2qsquare=2ksquare Ksquare=qsquare/2 Therefore,qsquare is divisible by 2 q is also divisible by 2. {Equation 2} From equation 1 and 2, P and q divides by 2 other than 1 This is contradictory to our assumption that p and q are co primes Therefore, √2 is a irrational number

1Thank You

Iron Man 6 years, 5 months ago

see R.S Aggrawal example

0Thank You

ANSWER

2/3. 1/3 2x - x. = 28

Posted by Amrita Sahoo 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Harman Jot 6 years, 5 months ago

,check your statement

0Thank You

ANSWER

x(2x+1)(x-2)(2x-3)=63

Posted by Arpita Saxsena 6 years, 5 months ago

CBSE > Class 10 > Mathematics

3 answers

Raghu?????? M 6 years, 5 months ago

1+1+1+1+1=5

0Thank You

Sagar Yadav 6 years, 5 months ago

Multiply all terms by 2 and then add or subtract and then answer =63 then find value of x

1Thank You

Iron Man 6 years, 5 months ago

multiply and find the value of x

2Thank You

ANSWER

What should be added to the polynomial 3 xrace to4-6 xrace2+4

Posted by Sanjay Nayak 6 years, 5 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

If 2x=secA, 2/x= tanA. Find 2(x^2-1/x^2)

Posted by Meet Jain 6 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 3 months ago

We know that
sec²A - tan²A = 1
{tex}\Rightarrow ( 2 x ) ^ { 2 } - \left( \frac { 2 } { x } \right) ^ { 2 }{/tex} = 1
{tex}\Rightarrow 4 x ^ { 2 } - \frac { 4 } { x ^ { 2 } }{/tex} = 1
{tex}\Rightarrow 4 \left( x ^ { 2 } - \frac { 1 } { x ^ { 2 } } \right){/tex} = 1
{tex}\Rightarrow \left( x ^ { 2 } - \frac { 1 } { x ^ { 2 } } \right) = \frac { 1 } { 4 }{/tex}

0Thank You

ANSWER

Is anyone's rich here please give me 800 rupees its urgent

Posted by Yukta Solanki 6 years, 5 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

The HCF of a and b is ?

Posted by Suraj Kumar 6 years, 5 months ago

CBSE > Class 10 > Mathematics

2 answers

Prashasti Prabhakar 6 years, 5 months ago

It's lcm Hcf is 1

0Thank You

Harshita Talib 6 years, 5 months ago

3Thank You

ANSWER

If we add 1 to number of fraction ot reduce to 1÷2.If we subtract 1 from the denominator it reduce 1÷3 represents situation algebraically and graphically.

Posted by Shashi Dhussa 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Iron Man 6 years, 5 months ago

you can sove this by asuuming x as a numerator and y as a denominator

0Thank You

ANSWER

Key answers of the class 10std board maths paper

Posted by Geetha Venkat Yadav 6 years, 5 months ago

CBSE > Class 10 > Mathematics

2 answers

?Niharika Sharma ? 6 years, 5 months ago

Of which year ????

1Thank You

Iron Man 6 years, 5 months ago

what are you saying

0Thank You

ANSWER

3x^2+40x-675=0

Posted by Aman Kumar 6 years, 5 months ago

CBSE > Class 10 > Mathematics

2 answers

Bhavya Mishra 6 years, 5 months ago

I dont know sorry

3Thank You

Iron Man 6 years, 5 months ago

you can solve this by Sridharacharya formula

1Thank You

ANSWER

Solve for x and y using Elimination method : 6(9x+6x)=3a+3b;7(bx-ay)=3a-2a

Posted by Suyeb Alam 6 years, 5 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Kya aap logon ne aaj ka test diya maths ka

Posted by Iron Man 6 years, 5 months ago

CBSE > Class 10 > Mathematics

3 answers

Masum Ansari 6 years, 5 months ago

0Thank You

Harshita Talib 6 years, 5 months ago

0Thank You

Akash Rajput 6 years, 5 months ago

Yees

2Thank You

ANSWER

One zero of the polynomials 3x cube + 16 x square + 15 x -18 is 2 by 3 find the The Other zeros of the polynomials

Posted by Suma N Sumaprakash 6 years, 5 months ago

CBSE > Class 10 > Mathematics

2 answers

Harshita Talib 6 years, 5 months ago

In this question x=2/3 X-2/3=0 3x-2=0 Then divide the polynomial by 3x-2

0Thank You

Harshita Talib 6 years, 5 months ago

Zeroes are -3 &-3

0Thank You

ANSWER

10 of the polynomial 3 x cube + 16 X square + 15 x minus 18 is 2 by 3 find the other zeros of the polynomials

Posted by Suma N Sumaprakash 6 years, 5 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

solve the equation 2x+3y=5 2x-3y=6

Posted by Mohd Kaif 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Iron Man 6 years, 5 months ago

By adding eqn 1and 2 we get 4x=11 thenx=11\4

1Thank You

ANSWER

If sinA+cosA=m and secA+cosecA=n than prove that n(m+1)(m-1)=2m

Posted by Neha Verma 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Neha Verma 6 years, 4 months ago

Please answer this question

0Thank You

ANSWER

Abdul travelled 300 km by train and 200 km by taxi it took him 5 hour 30 minutes but if he travells 260 km by train and 240 km by taxi he takes 6 minutes longer .find the speed of the train and that of the taxi

Posted by Arun Tyagi 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Prashasti Prabhakar 6 years, 5 months ago

Let the speed of ? be x And ? be. Y Then, Distance/speed= time 300/x+ 200/y = 11/2 min..................1 260/x +240/y = 11/2 + 1/10☺️☺️ Now solve this. You will get the answer

1Thank You

ANSWER

If sec A - tan A=4, THEN PROVE THAT cos A= 8/16

Posted by Rakhee Swarnkar 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 3 months ago

Now, sec A - tan A = 4........(i)
We know that
(sec A - tan A)(sec A + tan A) = 1
{tex}\Rightarrow{/tex} 4(secA + tanA) = 1
{tex}\Rightarrow{/tex} secA + tanA = {tex}\frac{1}{4}{/tex} .......(ii)
Adding (i) and (ii) we get,
2 secA = {tex}\frac{{17}}{4}{/tex}
{tex}\Rightarrow{/tex} secA = {tex}\frac{{17}}{8}{/tex}
{tex}\Rightarrow{/tex} cosA = {tex}\frac{8}{{17}}{/tex}