Question

If x + 1/x=2, find the value x^4-x^3

Answer 1

Answer:

x+1x=4∣⋅x

x2+1=4x∣−4x

x2−4x+1=0∣(a±b)2=a2±2ab+b2

(x−2)2−3=0∣+3

(x−2)2=3∣√

x−2=±3–√∣+2

x=2±3–√

but for these values:

x2+1x3=11⋅(3∓3–√)≠12

so there is no solution.

As for x2+1x3=12 see