Explanation

Given:

x + 1/x = 10

Squaring both sides:

(x + 1/x)^2 = 10^2

x^2 + 2(x)(1/x) + 1/x^2 = 100

x^2 + 2 + 1/x^2 = 100

Subtract 2 from both sides:

x^2 + 1/x^2 = 98