## Question

`If a + b = 5 and ab = 6, find a`^{2} + b^{2}.

`If a + b = 5 and ab = 6, find a`^{2} + b^{2}.

A. 12

B. 13

C. 8

D. 16

**Answer: B. 13**

**Solution:**

(a+b)^{2} = a^{2} + b^{2} + 2ab

⇒ (5)^{2} = a^{2} + b^{2} + 2×6

⇒ 25 = a^{2} + b^{2} + 12

⇒ 25 − 12 = a^{2} + b^{2}

⇒ 13 = a^{2}+b^{2}

**∴ a ^{2} + b^{2} = 13**

**Hence, The Answer a ^{2} + b^{2} = 13.**

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