Question

x²+1/x² and (x-1/x)² , when x+1/x = 8​

Answer 1

Answer:

Step-by-step explanation:

Given ,

x-(1/x) = 3/2 ———(1)

Now,

[x+(1/x)]^2 = [x-(1/x)]^2 + 4x * (1/x) = (3/2)^2 + 4 = 9/4 + 4 = (16+9)/4 = 25/4

x+(1/x) = √(25/4) = 5/2 ——-(2)

x^2 - (1/x)^2

= [x+(1/x)] * [x-(1/x)]

Put (1) & (2),

= 5/2 * 3/2

= 15/4 (ans)