Question

If m^2+m^-2=23;then what is the value of m^3+m^-3?

Answer 1

this will be the answer

Answer 2

Answer: 110

Step-by-step explanation:

Given- m^2 + m^-2 = 23

Step 1    →     m^2 + 1/m^2 = 23

Both side +2

           ( m^2 + 1/m^2) + 2 = 23+2

             (m^2 + 1/m^2) + 2 = 25

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

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

step 2 →   So   (m^2 + 1/m^2) + 2 = 25

                             (m + 1/m)^2 = 25

                                (m + 1/m) = √25

                         (m + 1/m) = 5-----------(1)

Formula - (m + 1/m)^3 = m^3 + 1/m^3 + 3* m^3*1/m^3 (m+1/m)

(m + 1/m)^3 = m^3 + 1/m^3 + 3* (m+1/m)

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

        → put the value from eq. (1)

                     m^3 + 1/m^3 = ( 5)^3 - 3*5

                    m^3 + 1/m^3 = 125 - 15

                     m^3 + 1/m^3 = 110