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

Question

If a + b = 5 and ab = 6, find a2 + b2.

A. 12

B. 13

C. 8

D. 16

Answer: B. 13

Solution:

(a+b)² = a² + b² + 2ab

⇒ (5)² = a² + b² + 2×6

⇒ 25 = a² + b² + 12

⇒ 25 − 12 = a² + b²

⇒ 13 = a²+b²

∴ a² + b² = 13

Hence, The Answer a² + b² = 13.

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