If: \(a + b + c = 14\) and \(a^2 + b^2 + c^2 = 96\), then \((ab + bc + ca)\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 50
The identity \((a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)\) links the three given quantities, so \(ab+bc+ca\) can be found without knowing \(a\), \(b\) and \(c\).
Squaring the given sum: \((a+b+c)^2=14^2=196\)
Putting 196 and \(a^2+b^2+c^2=96\) into the identity: \(196=96+2(ab+bc+ca)\)
\(2(ab+bc+ca)=100\), so \(ab+bc+ca=50\)