Question

x^2+1/x^2=27,find (x^2-1/x^2)

Answer 1

Hi ,

x² + 1/x² = 27----( 1 )

add 2 both sides, we get

x² + 1/x² + 2 = 27 + 2

(x + 1/ x )² = 29-----( 2 )

ii ) subtract 2 both sides of equation ( 1 )

x² + 1 / x² - 2 = 27 - 2

( x - 1/ x )² = 25 -------( 3 )

multiply ( 2 ) and ( 3 ) ,

( x + 1/ x )² ( x - 1 / x)² = 29 × 25

[ (x + 1/x)(x -1/x)]² = 29 × 25

x² - 1/x² = √29 × ( 5 × 5 )

= 5√29

I hope this helps you.

:)