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Question -

If a + b = 7 and ab = 12, find the value of a2 + b2.



Answer -

a + b = 7, ab = 12
Squaring both sides,
(a + b)2 = (7)2
⇒ a2 + b2 + 2ab = 49
⇒ a2 + b2 + 2 x 12 = 49
⇒ a2 +b2 + 24 = 49
⇒ a2 +b2 = 49 – 24 = 25
∴ a2 +b2 = 25

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