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For the two positive numbers a , b , if a , b and 1 18 are in a geometric progression, while 1 a , 10 and 1 b are in an arithmetic progression, then, 16 a + 12 b is equal to _____ .

Correct answer

0

Step-by-step solution

Since, a , b , 1 18 are in GP, so a 18 = b 2 ⇒ a = 18 b 2       . . . . 1 Also, 1 a , 10 , 1   b are in A.P., so 1 a + 1 b = 20 ⇒ a + b = 20 a b ⇒ 18 b 2 + b = 360 b 3 ⇒ 360 b 2 - 18 b - 1 = 0        ∵     b ≠ 0 ⇒ b = 18 ± 324 + 1440 720 ⇒     b = 18 + 1764 720        ∵   b > 0 ⇒   b = 1 12 ⇒ a = 18 × 1 144 = 1 8 Now, 16 a + 12 b = 16 × 1 8 +

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