Question

if (x + 1/ x) = 12 , find the value of x²-1/x²

Answer 1

Answer:

24√35

Step-by-step explanation:

x + 1/x = 12

on square both sides ,we get

(x + 1/x)^2 = 144

x^2 + 1/x^2 + 2(x)(1/x) + 2(x)(1/x) - 2(x)(1/x) = 144

(x - 1/x)^2 = 144 - 4

(x - 1/x)^2 = 140

x - 1/x = √140

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

= 12 × √140 = 12 × √( 7 × 2 × 5 × 2 )

= 24√35 Answer