Question

if x+1/x= 10 then find the value of x^2-1/x^2

Answer 1

GIVEN:

$x + \frac{1}{x} = 10$

TO FIND :

${x}^{2} + \frac{1}{ {x}^{2} }$

SOLUTION:

Squaring both sides,

${(x + \frac{1}{x} )}^{2} = {(100) }^{2}$

${(x)}^{2} + 2 \times x \times \frac{1} {x} + { (\frac{1}{x}) }^{2} = 100$

${x}^{2} + 2 + \frac{1}{ {x}^{2} } = 100$

${x}^{2} + \frac{1}{ {x}^{2} } = 100 - 2$

${x}^{2} + \frac{1}{ {x}^{2} } = 98$