Question

If x^2+1/x^2=7 find x-1/x

Answer 1

TOPIC :- POLYNOMIAL

FORMULA

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

Applying the second formula , we get

$( {x - \frac{1}{x} )}^{2} = 7 - 2 \\ ( \: {x - \frac{1}{x}) }^{2} = 5 \\ \\ x - \frac{1}{x} = + - \sqrt{5}$

Answer 2

Given :

x² + 1 / x² = 7

It can be written as

=> x² + ( 1 / x )² = 7

Subtracting 2( x )( 1 / x ) on both sides

=> x² + ( 1 / x )² - 2( x )( 1 / x ) = 7 - 2( x )( 1 / x )

Using algebraic identity ( a - b )² = a² + b² - 2ab,

=> ( x - 1 / x )² = 7 - 2

=> ( x - 1 / x )² = 5

Taking square root on both sides

=> x - 1 / x = ± √5

Therefore the value of x - 1 / x is ± √5.