Question

Given that `(a+b)^2 = 189` and `6ab = 78`, what is the value of `3(a^2+b^2)`?

Answer 1

I tried this:

Explanation:

We have:
`(a+b)^2=189`
`a^2+2ab+b^2=189`
let us multiply and divide by `3`:
`color(red)(3/3)(a^2+2ab+b^2)=189`
`3a^2+6ab+3b^3=3*189`

but `6ab=78`

so:
`3a^2+78+3b^3=3*189`
`3(a^2+b^2)=-78+567`
`3(a^2+b^2)=489`