If \(a=925\), \(b=924\) and \(c=923\), then find the value of \(3(a^2+b^2+c^2-ab-bc-ca)\).
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 9
The expression in the bracket can be written with the differences alone: \(a^2+b^2+c^2-ab-bc-ca=\frac{1}{2}\left[(a-b)^2+(b-c)^2+(c-a)^2\right]\), so the large numbers never need to be squared.
\(a-b=1\), \(b-c=1\), \(c-a=-2\)
\(a^2+b^2+c^2-ab-bc-ca=\displaystyle\frac{1}{2}(1+1+4)=3\)
\(3\times3=9\)