Question

x² + 1/x² = 23, evaluate:
1. x + 1/x
2. x-1/x

Answer 1

Answer:

1.)x+1/x

(x+1/x)²=x²+1/x²+2×x×1/x

(x+1/x)²=23+2

(x+1/x)²=25

x+1/x=

$\sqrt{2} 5$

x +1/x=5

2.)x-1/x

(x-1/x)²=x²+1/x²-2×x×1/x

(x-1/x)²=23-2

(x-1/x)²=21

x-1/x=

$\sqrt{21}$