Question

If x²+1/x² = 51 find x

Answer 1

x² + 1/x² = 51

Adding 2 on both sides

(x+1/x)² = 53

x + 1/x = √53       .........(1)

Now
x² + 1/x² = 51

Subtracting 2 on both sides

(x-1/x)² = 49

x - 1/x = 7       .........(2)

Adding both equations,

2x = 7 + √53

2x = 7 + 7.28

2x = 14.28

x = 7.14