Question

if x2+1x2=7,find the value of x3+1/x3,taking only the positive value of x+1/x

Answer 1

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!

Answer 2

(x + 1/x)^2= x^2+ 1/x^2+ 2
(x + 1/x)^2= 9
x + 1/x = 3
now(x + 1/x)^3= x^3+ 1/x^3+ 3(x + 1/x)
27 = x^3+ 1/x^3+ 9
x^3+ 1/x^3= 27 - 9 = 18