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 larger part be x.

Then, the smaller part =16−x

By hypothesis, we have 2x2= (16−x)2 + 164

⇒ x2 + 32x − 420 = 0

⇒ (x + 42) (x−10) = 0

⇒ x = −42 or x = 10

∵ x can not be a negative

⇒ x = 10

hence, the required parts are 10 and (16−10)=6

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