Question

(x-1/x)³ = x³-1/x³ - 3×x×1/x(1–1/x) or (x-1/x)³ = x³-1/x³ - 3(1–1/x) or (x-1/x)³ = 14 - 3(1–1/x) . . . . [Given, x³-1/x³ = 14] Let x-1/x = a Therefore a³ = 14 - 3a or a³+3a-14 =0 or a³-2a²+2a²-4a+7a-14 =0 or a²(a-2) +2a(a-2) +7(a-2) =0 or (a-2)(a²+2a+7) =0 or a-2 = 0/(a²+2a+7) or a = 2 So x-1/x = 2​

Answer 1

Answer:

Hello (x-1/x)³ = x³-1/x³ - 3×x×1/x(1–1/x)

or (x-1/x)³ = x³-1/x³ - 3(1–1/x)

or (x-1/x)³ = 14 - 3(1–1/x) . . . . [Given, x³-1/x³ = 14]

Let x-1/x = a

Therefore a³ = 14 - 3a

or a³+3a-14 =0

or a³-2a²+2a²-4a+7a-14 =0

or a²(a-2) +2a(a-2) +7(a-2) =0

or (a-2)(a²+2a+7) =0

or a-2 = 0/(a²+2a+7)

or a = 2

So x-1/x = 2