Problem
ALG-B2-M06-P001 Squares through p and q
#1
★★☆☆☆ Level 2 of 5
Let \(p=a+b+c\), \(q=ab+bc+ca\). Prove \[a^2+b^2+c^2=p^2-2q.\]
Hint. Expand \((a+b+c)^2\).
\(p^2=(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)=\sum a^2+2q\). Hence \(\sum a^2=p^2-2q\).
The first required technical skill of the module.