if x^4 + 1/x^4 =42 .find x+1/x

Answer 1

(x + 1/x)^4 = x^4 + 1/x^4 + 4(x^2 + 1/x^2) + 6
= 48 + 4(x^2 + 1/x^2)

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

So, letting u = x + 1/x

x^4 + 1/x^4 = 42 = u^4 - 4u^2 + 2

u^4 - 4u^2 - 40 = 0
u^2 = 2 ± 2√11

so,

x + 1/x = ±√(2±2√11)

Better double-check the steps; it's messy