Question

if x+1/x=17/4 , find the value of x²-1/x²

Answer 1

Answer:

x²-1/x²=255/16

Step-by-step explanation:

(x+1/x)²=x²=1/x²+2(x)(1/x)

(17/4)²=x²+1/x²+2

289/16 - 2=x²+1/x²

by taking LCM

(289-32)/16=x²+1/x²

257/16=x²+1/x²

now

(x-1/x)²=x²+1/x² -2

(x-1/x)²=257/16 - 2

(x-1/x)²=(257-32)/16

(x-1/x)²=225/16

(x-1/x)=15/4

Using the identity

x²-1/x²=(x+1/x)(x-1/x)

x²-1/x²=(17/4)(15/4)

x²-1/x²=255/16