If \(a-b=3\) and \(ab=28\), consider the following statements:
I. \(a^2+b^2=65\)
II. \((a+b)^2=121\)
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both I and II
Use \(a^2+b^2=(a-b)^2+2ab\) and \((a+b)^2=(a-b)^2+4ab\).
Statement I — Correct.
\(a^2+b^2=3^2+2\times28=9+56=65\)
Statement II — Correct.
\((a+b)^2=3^2+4\times28=9+112=121\)
Both statements are correct.