Question

Divide 16 in two parts such that 2 times the square of larger part is 164 more then the square of smallest part

Answer 1

Let the smaller part be x.

∴ The larger part is (16 – x).

Given, 2 × (Larger  part)2 = (Smaller part)2 + 164

∴ 2 (16 – x)2 = x2 + 164

⇒ 2 (256 – 32x + x2) = x2 + 164

⇒ 512 – 64x + 2x2 = x2 + 164

⇒ x2 – 64x + 348 = 0

⇒ x2 – 58x – 6x + 348 = 0

⇒ x (x – 58) –6 (x – 58) = 0

⇒ (x – 58) (x –6) = 0

⇒ x – 58 = 0 or x – 6 = 0

⇒ x = 58 or x = 6

⇒ x = 6  (�x cannot be 58)

∴ Smaller part = x = 6

Larger part = 16 – x =16 – 6 = 10

Cheers!