If 2a + 3b = 7 and ab = 2, find 4a2 + 9b2.
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We know that,
a2 + b2 = (a + b)2 - 2ab.
∴ 4a2 + 9b2 = (2a)2 + (3b)2 = (2a + 3b)2 - 12ab.
Substituting values we get,
⇒ 4a2 + 9b2 = (7)2 - 12 × 2
⇒ 4a2 + 9b2 = 49 - 24
⇒ 4a2 + 9b2 = 25.
Hence, 4a2 + 9b2 = 25.
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