Question

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

Answer 1

We need to divide 16 into two parts.

Let the two parts be x and 16 - x.

Given that Twice the square of larger part exceeds the square of the smaller part by 164.


= > 2x^2 = (16 - x)^2 + 164

= > 2x^2 - (16 - x)^2 = 164

= > 2x^2 - (256 + x^2 - 32x) = 164

= > 2x^2 - 256 - x^2 + 32x = 164

= > x^2 + 32x - 420 = 0

= > x^2 + 42x - 10x - 420 = 0

= > x(x + 42) - 10(x + 42) = 0

= > (x - 10)(x + 42) = 0

= > x = 10, x = -42


Therefore,

Larger part = 10.

Smaller part = 16 - 10

                     = 6.




Hope this helps!