Question

x-1/x=√2 find x=1/x find a) x²+1/x² b)x+1/x c)x³+1/x³

Answer 1

Answer:

a) 4 b) $\sqrt{6}$ c) 3$\sqrt{6}$

Step-by-step explanation:

a) x-1/x = $\sqrt{2}$

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

($\sqrt{2}$)^2+2 = x^2+1/x^2

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

x^2+1/x^2 = 4

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

x+1/x = $\sqrt{4+2}$

x+1/x = $\sqrt{6}$

c) (x+1/x)^3 = x^3+1/x^3+3(x+1/x)

($\sqrt{6}$)^3 = x^3+1/x^3+3$\sqrt{6}$

6$\sqrt{6}$-3$\sqrt{6}$ = x^3+1/x^3

x^3+1/x^3 = 3$\sqrt{6}$