Question

Suppose a b equals 6 and (a + b)squared = 20 what is a squared + b squared?

Answer 1

We can write the equivalencies between this terms using the binomial expansion for (a+b)^2:

$\begin{gathered} (a+b)^2=a^2+2ab+b^2 \\ (a+b)^2=(a^2+b^2)+2ab \\ a^2+b^2=(a+b)^2-2ab \\ a^2+b^2=20-2\cdot6 \\ a^2+b^2=20-12 \\ a^2+b^2=8 \end{gathered}$

Answer: The value of a^2+b^2 is 8.