Question

if x-1/x=7 then find the value of x^2+1/x^2

Answer 1

Given

x - 1/x = 7

To find

x^2 + 1/x^2

Solution

( x - 1/x )^2 = ( x )^2 + ( 1/x )^2 - 2 ( x )( 1/x )

= x^2 + 1/x^2 - 2

since ( a - b )^2 = a^2 + b^2 - 2ab

( x - 1/x )^2 = x^2 + 1/x^2 - 2

( 7 )^2 = x^2 + 1/x^2 - 2

49 = x^2 + 1/x^2 - 2

x^2 + 1/x^2 = 49 + 2

x^2 + 1/x^2 = 51