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ANSWER

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Posted by Arpan Narain 20 hours ago

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Preeti Dabral 20 hours ago

Let p be any positive integer and b = 3. Applying division Lemma with p and b =3 ,

we have

p = 3q + r, where 0 {tex}\leq{/tex} r < 3 and q is some integer

So r=0,1,2

If r=0 , p=3q

If r=1, p=3q+1

If r=2, p=3q+2

Therefore any positive integer is of form 3q,3q+1,3q+2 for some integer q.

Posted by Priyanshu Pawar 1 day, 14 hours ago

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Posted by Priyanshu Pawar 1 day, 14 hours ago

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Posted by Surendera Kumar.S 1 day, 15 hours ago

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Himanshi Gautam 1 day, 1 hour ago

4-5√3= a/b
-5√3= a/b-4
√3=4/5-a/b
RHS is not equal to LHS
HENCE IT IS AN IRRATIONAL NUMBER.

Posted by Mehtab Sheikh 1 day, 17 hours ago

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Posted by Baddam Meena Reddy 1 day, 18 hours ago

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Posted by Megha Vishwakarma 1 day, 23 hours ago

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Preeti Dabral 1 day, 23 hours ago

Suppose the numerator of the fraction be x

Denominator of the fraction be y

{tex}\therefore{/tex} the fraction is {tex}\frac{x}{y}{/tex}

According to the question,

The sum of the numerator and denominator of the fraction is 12.

{tex}\Rightarrow x + y = 12{/tex}

{tex}\Rightarrow{/tex} {tex}x + y - 12 = 0{/tex}

If the denominator is increased by 3, the fraction becomes {tex}\frac{1}{2}{/tex}.

{tex}\Rightarrow \frac{x}{{y + 3}} = \frac{1}{2}{/tex}

{tex}\Rightarrow{/tex} {tex}2x = (y + 3){/tex}

{tex}\Rightarrow{/tex} {tex}2x - y - 3 = 0{/tex}

So, we have two equations

{tex}x + y - 12 = 0{/tex}

{tex}2x - y - 3 = 0{/tex}

Here x and y are unknowns.

We have to solve the above equations for x and y.

By using cross-multiplication,

{tex}\Rightarrow \frac{x}{{(1) \times ( - 3) - ( - 1) \times - 12}}{/tex} {tex} = \frac{{ - y}}{{1 \times ( - 3) - 2 \times - 12}}{/tex} {tex}= \frac{1}{{1 \times ( - 1) - 2 \times (1)}}{/tex}

{tex}\Rightarrow \frac{x}{{ - 3 - 12}}{/tex} {tex}= \frac{{ - y}}{{ - 3 + 24}} = \frac{1}{{ - 1 - 2}}{/tex}

{tex}\Rightarrow \frac{x}{{ - 15}} = \frac{{ - y}}{{21}} = \frac{1}{{ - 3}}{/tex}

{tex}\Rightarrow \frac{x}{{15}} = \frac{y}{{21}} = \frac{1}{3}{/tex}

{tex}\Rightarrow x = \frac{{15}}{3},\;y = \frac{{21}}{3}{/tex}

{tex}\Rightarrow{/tex} {tex}x = 5, y = 7{/tex}

The fraction is {tex}\frac{5}{7}{/tex}

Posted by Armaan Hizkiel 1 day, 23 hours ago

- 1 answers

Preeti Dabral 1 day, 23 hours ago

Given :

To Find : solve it by cross multiplication method

Solution:

**Cross multiplication method**

**Equations : **

Comparing the given equations

So, x = 4 and y = 1

Posted by Harsh Kushwah 1 day, 23 hours ago

- 3 answers

Preeti Dabral 1 day, 23 hours ago

<header>

Consider quadratic polynomial

P(x) = 2x^{2} – 16x + 30.

Now, 2x^{2} – 16x + 30 = (2x – 6) (x – 3)

= 2 (x – 3) (x – 5)

The zeros of P(x) are 3 and 5.

Sum of the zeros = 3 + 5 = 8 = −(−16)2 = -[coefficient of xcoefficient of x2]

Product of the zeros = 3 × 5 = 15 = 302 = [constant term coefficient of x2]

So if ax^{2} + bx + c, a ≠ 0 is a quadratic polynomial and α, β are two zeros of polynomial then

α+β=−ba

αβ=ca

In general, it can be proved that if α, β, γ are the zeros of a cubic polynomial ax^{3} + bx^{2} + cx + d, then

α+β+γ=−ba

αβ+βγ+γα=ca

αβγ=−da

Note: ba, ca and da are meaningful because a ≠ 0.

Armaan Armaan 1 day, 22 hours ago

Zeroes are number like a and b.
Coefficient are numbers side the x and y. 😉

Posted by Dhruv Lad 2 days, 1 hour ago

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Aditya Raghuwanshi 1 day, 3 hours ago

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Posted by Ayush Rai 2 days, 15 hours ago

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Vinayak Rathod Vishal 2 days, 4 hours ago

Find the 6th term from the end of the A. P 17,14 , 11...-40

Akarshit Sharma 2 days, 15 hours ago

3/5=0.6
4/5=0.8
So numbers between between 0.6 and 0.8 are 0.65 , 0.70 , 0.71 , 0.75 , 0.61

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Aditya Raghuwanshi 1 day, 3 hours ago

- Don't post personal information, mobile numbers and other details.
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