Let 1 16 , a and b be in G.P. and 1 a , 1 b , 6 be in A.P., where a , b 0 . Then 72 ( a + b ) is equal to _______ .

Question

Let 1 16 , a and b be in G.P. and 1 a , 1 b , 6 be in A.P., where a , b > 0 . Then 72 ( a + b ) is equal to _______ .,

MARKS App · Accepted Answer

a 2 = b 16 ⇒ 1 b = 1 16 a 2 2 b = 1 a + 6 1 8 a 2 = 1 a + 6 1 a 2 - 8 a - 48 = 0 1 a = 12 , - 4 ⇒ a = 1 12 , - 1 4 a = 1 12 , a > 0 b = 16 a 2 = 1 9 ⇒ 72 ( a + b ) = 6 + 8 = 14

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