If a + b = 5 and a^2 + b^2 = 13, find ab.

Question

If a + b = 5 and a^2 + b^2 = 13, find ab.

A. 6

B. -6

C. 12

D. -12

Answer: A. 6

Solution:

Given,
a + b = 5 and a^2 + b^2 = 13,

On squaring a + b = 5 both sides, we get
(a+b)² = (5)²

⇒ a² + b² + 2ab = 25

⇒ 13 + 2ab = 25

⇒ 2ab = 25 − 13 = 12

⇒ ab = 12/2 = 6

∴ab = 6

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