If \(m-n=16\) and \(m^2 + n^2 = 400\), the value of \(mn\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 72
The identity \((m-n)^2=m^2+n^2-2mn\) links the three given quantities, so \(mn\) can be found without finding \(m\) and \(n\).
\(16^2=400-2mn\)
\(256=400-2mn\)
\(2mn=144\)
\(mn=72\)