Question

if x=2^1/3+2^-1/3 then find 2x^3-6x-5​

Answer 1

Answer:

if x=2^1/3+2^-1/3 then find 2x^3-6x-5​?

Step-by-step explanation:

Let the cube root of 2 be y.

=>x = y + 1/y

=>2x^3 = 2(y + 1/y)^3

            = 2(y^3 + 1/y^3 + 3y + 3/y)

            = 2(y^3 + 1/y^3) + 6(y + 1/y)

Note that y^3 = 2.

=> 2x^3 = 2(2 + 1/2) + 6x                              (y + 1/y = x as mentioned above)

             = 5 + 6x

i hope that this helps you. have a good day.