Question

x^2+1/x^2=23. find x^3+1/x^3

Answer 1

Given x^2 + 1/x^2 = 23.  ------- (1)
 
We know that (a + b)^2 = a^2 + b^2 + 2ab.

                        (x + 1/x)^2 = x^2 + 1/x^2 + 2 * x * 1/x

                                         = x^2 + 1/x^2 + 2.    ------- (2)

Substitute (1) in (2)

x^2  + 1/x^2 + 2 = 23 + 2

                          = 25

(x + 1/x)^2 = 25

x + 1/x = 5.


Given x^3 + 1/x^3 = (x + 1/x)(x^2 - 1 + 1/x^2)

                              = 5 * (23 - 1)

                              = 5 * 22

                              = 110.


Therefore x^3 + 1/x^3 = 110.


Hope this helps!

Answer 2

Answer:

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