Question

if, x+1/x=3,find the value of x^2+1/x^2

Answer 1

$x + \frac{1}{x} = 3 \\ \\ \\ \\ \boxed{\bold{ \underline{square \: on \: both \: sides}}} \\ \\ \\ \\ {(x + \frac{1}{x}) }^{2} = {3}^{2} \: \: \: \\ \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2(x \times \frac{1}{x} ) = 9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | \bold{ \: {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab} \\ \\ \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9 \\ \\ \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2 \\ \\ \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 7$

Answer 2

Hey there!

Given, $\boxed{x + \frac{1}{x} = 3 }$

Now We have to find value of x² + 1/x²

=> x² + 1/x²

=> ( x + 1/x)² - 2x(1/x)

We know that, x + 1/x = 3 , x × 1/x = 1

=> 3² - 2

=> 9 -2

=> 7 .

Also,

( x + 1/x) = 3

Square on both sides,

( x + 1/x)² = 3²

x² + 1/x² + 2 = 9

x² + 1/x² = 9 - 2 = 7

Therefore, $\boxed{ x^2 + \frac{1}{x^2} = 7}$