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Question -

If a – b = 5 and ab = 12, find the value of a2 + b2 .



Answer -

a – b = 5, ab = 12
Squaring both sides,
⇒ (a –b)2 = (5)2
⇒ a2 + b2 – 2ab = 25
⇒ a2 + b2 – 2 x 12 = 25
⇒ a2 + b2 – 24 = 25
⇒ a2 + b2 = 25 + 24 = 49
∴ a2 +b2 = 49

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