The sum of square of a positive number and square of its reciprocal is 7.Find the number

Answer 1

n^2 + 1/n^2 = 7

n^4 + 1 = 7 n^2
... n^4 - 7 n^2 + 1 = 0

let k = n^2

k^2 - 7k + 1 = 0

use quadratic formula to find k

n = √k