Question

20. Divide 16 into two parts such that twice the square of the larger part
exceeds the square of the smaller part by 164.
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Answer 1

Answer:

Let x and (16 - x) are two parts of 16 where (16 - x) is longer and x is smaller .

A/C to question,

2 × square of longer = square of smaller + 164

⇒ 2 × (16 - x)² = x² + 164

⇒ 2 × (256 + x² - 32x ) = x² + 164

⇒ 512 + 2x² - 64x = x² + 164

⇒ x² - 64x + 512 - 164 = 0

⇒ x² - 64x + 348 = 0

⇒x² - 58x - 6x + 348 = 0

⇒ x(x - 58) - 6(x - 58) = 0

⇒(x - 6)(x - 58) = 0

⇒ x = 6 and 58