Problem
ALG-B2-M09-P015 Two fixed sums
#15
★★★★☆ Level 4 of 5
Let \(a+b+c=3\) and \(ab+bc+ca=2\). Find \(a^2+b^2+c^2\).
Hint. Use \((a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)\).
\(a^2+b^2+c^2=(a+b+c)^2-2(ab+bc+ca)=9-4=5\). The answer is \(5\).
Simple but important relation between fixed \(p\) and \(q\).