Mathematics
If (3a + 4b) = 16 and ab = 4, find the value of (9a2 + 16b2).
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Answer
⇒ (3a + 4b)2 = (3a)2 + (4b)2 + 2 × 3a × 4b
⇒ (3a + 4b)2 = 9a2 + 16b2 + 24ab
⇒ 9a2 + 16b2 = (3a + 4b)2 - 24ab
Given,
(3a + 4b) = 16 and ab = 4
Substituting values we get :
⇒ 9a2 + 16b2 = (16)2 - 24 × 4
⇒ 9a2 + 16b2 = 256 - 96
⇒ 9a2 + 16b2 = 160.
Hence, 9a2 + 16b2 = 160.
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