Question

If x²+1/x²=7 find the value of x³+1/x³ taking only the positive value of x+1/x
value of x³+1)x³taking only the positive value of x+1/x

Answer 1

Step-by-step explanation:

Given Equation is x^2 + 1/x^2 = 7

We know that (x + 1/x)^2 = x^2 + 1/x^2 + 2 * x * 1/x

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

                                        = 7 + 2

                                        = 9

                          (x + 1/x) = 3

Now,

(x^3 + 1/x^3) = (x + 1/x)^3 - 3 * x * 1/x * (x + 1/x)

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

 

                    = (3)^3 - 3(3)

                   = 27 - 9

                   = 18.