Question

√5-2/√5+2,then (x^4+1/x^4)=?

Answer 1

By rationalizing,

x = 9 - 4√5

1/x = 1/(9-4√5)

Again by rationalizing,

1/x = 9+4√5

x⁴ + 1/x⁴ = ((x + 1/x)² - 2)² - 2

x + 1/x = (9-4√5) + (9+4√5)

= 18

x⁴ + 1/x⁴ = ((18)²-2)² - 2

= 322² - 2 = 103682