If \(a+b=8\) and \(ab=15\), match List-I with List-II.
| List-I (Expression) | List-II (Value) | ||
|---|---|---|---|
| (A) | \(a^2+b^2\) | (I) | 120 |
| (B) | \((a-b)^2\) | (II) | 34 |
| (C) | \(a^3+b^3\) | (III) | 4 |
| (D) | \(a^2b+ab^2\) | (IV) | 152 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
Write every expression in terms of \(a+b=8\) and \(ab=15\).
(A) \(a^2+b^2=(a+b)^2-2ab=64-30=34\) → (II)
(B) \((a-b)^2=(a+b)^2-4ab=64-60=4\) → (III)
(C) \(a^3+b^3=(a+b)^3-3ab(a+b)=512-360=152\) → (IV)
(D) \(a^2b+ab^2=ab(a+b)=15\times8=120\) → (I)
So the matching is (A)-(II), (B)-(III), (C)-(IV), (D)-(I).