Question

if x2 +1/x2 =7, find x3 + 1/x3 using positive value of X+1/X


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Answer 1

Answer:

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.

Hope this helps!