Question

if x + 1/x = 2 then prove that x²+1/x²=2​

Answer 1

Step-by-step explanation:

x + 1/x = 2

Squaring both sides,

(x + 1/x)² = 2²

=> x² + 1/x² + 2×x×1/x = 4

=> x² + 1/x² = 4-2 =2

Hence, proved.

Answer 2

Step-by-step explanation:

Given that :—

$\mathrm{If \: x + \frac{1}{x} = 2 \: then \: prove \: that \: {x}^{2} + \frac{1}{ {x}^{2} } = 2.}$

Solution :—

Let's solve the problem

We have,

$\mathrm{x + \frac{1}{x} = 2}$

Squaring on both sides, we get

$\mathrm{ \bigg(x + \frac{1}{x} \bigg)^{2} = {2}^{2} }$

$⟹ \mathrm{{x}^{2} + 2( \cancel{x}) \bigg( \frac{1}{ \cancel{x}} \bigg) + \bigg( \frac{1}{x} \bigg)^{2} } = 4$

$⟹ \mathrm{{x}^{2} + 2 + \frac{1}{ {x}^{2} } = 4}$

$⟹ \mathrm{ {x}^{2} + \frac{1}{ {x}^{2} } = 4 - 2}$

$⟹ \mathrm{ {x}^{2} + \frac{1}{ {x}^{2} } = 2 }$

Hence, proved

Answer:—

$\mathrm{Hence,the \: value \: of \: {x}^{2} + \frac{1}{ {x}^{2} } \: is \: 2.}$

Used formulae :—

• (a+b)² = a² + 2ab + b².

Learn more;

# Brainly

1. If x=√3a+2b + √3a-2b / √3a+2b - √3a-2b

prove that bx²-3ax+b=0

https://brainly.in/question/19664646

Date| wed | May | 26 |.