If \(a+b=7\) and \(ab=10\), consider the following statements:
I. \(a^2+b^2=31\)
II. \(a^3+b^3=133\)
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Only II
Write both expressions in terms of \(a+b\) and \(ab\): \(a^2+b^2=(a+b)^2-2ab\) and \(a^3+b^3=(a+b)^3-3ab(a+b)\).
Statement I — Incorrect.
\(a^2+b^2=7^2-2\times10=49-20=29\), not 31
Statement II — Correct.
\(a^3+b^3=7^3-3\times10\times7=343-210=133\)
Only statement II is correct.