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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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