[Mark]

Can you please help me solve?
If M+N=3 and M^2+N^2=6, Find the numerical value for
M(cubed)+N (cubed).

[MathMaven53]

We are given M+N=3 and M^2 + N^2 =6

Factor M^3 + N^3

M^3 + N^3 = (M+N)(M^2 -MN + N^2)

= (M+N)(M^2 + N^2 - MN)

We have all quantities on the right side except MN

To find it, square M + N = 3

M^2 + 2MN + N^2 = 9

Substituting for M^2 + N^2 and solving for MN gives

MN= 3/2

Then


M^3 + N^3 = (M+N)(M^2 + N^2 - MN)

= 3(6 - 3/2)

= 27/2