### 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}

⇒ a^{2 }+ b^{2 }+ 2ab = 25

⇒ 13 + 2ab = 25

⇒ 2ab = 25 − 13 = 12

⇒ ab = 12/2 = 6

**∴ab = 6**

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