Question

if m-1/m= 5 find m3-1/m3

Answer 1

Answer:

Answer:

m - (1/m)=5 <=> ((m^2) - 1)/m=5 <=> (m^2) - 5m - 1 = 0

Now you just need to solve the quadratic equation for m. It will have two roots:

m' = [5 + sqrt(29)]/2

and

m" = [5 - sqrt(29)]/2

Notice that m'>0 and m"<0. I will choose m', the first root of the equation because m' is clearly positive. But if you want to, later you can solve the equation with m" too....

Now you multiply with the conjugate of m - (1/m), that is m + (1/m), to the both sides of the equality:

[m + (1/m)]*[m - (1/m)] = 5*[m + (1/m)] <=> [(m^2) - 1/(m^2)] = 5*[m + (1/m)]

Notice that now we have what was asked. We have [(m^2) - 1/(m^2)] in the first part of the equality. Now you just need to put the value of m' in m, that we found, and solve the second side of the equation. Solving the second side of the equality, we can conclude that:

[(m^2) - 1/(m^2)] = 10 - 3*sqrt(29)

I hope i could help...