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

Question

Represent the following situations in the form of the quadratic equation.

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

Answer 1

Let ‘x’ be the one part and the other part will be 16 − x.

[∵ 16 is being divided]

∵ Twice of the square of larger part exceeds the square of the smaller part by 164.

∴ 2x² = (16 – x)² + 164

∴ 2x² = 256 – 32x + x² + 164

⇒ x² + 32x − 420 = 0