Question

Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164.​

Answer 1

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Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164.

Let the largest part be x. Then, the smaller part =16-x.

By hypothesis , We have

2x^{2} = ( 16 - x ) ^ {2} + 164

↦ 2x^{2} - ( 16 - x ) ^ {2} - 164 = 0

↦ x{2} + 32 x - 420 = 0

↦ ( x + 42 ) ( x - 10 ) = 0

↦ x = -42 or, x = 10

↬ x = 10 [ ∵ x > 0 ∴ x = -42 is not possible]

Hence , the required parts are 10 are 6.

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