Question

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

Answer 1

Let the smaller part be x
Hence the larger part is (16 – x)
Given 2(16 – x)2 = x2 + 164
⇒ 2( 256 – 32x + x2) =  x2 + 164
⇒ 512 – 64x + 2x2 –  x2 – 164 = 0
⇒ x2– 64x + 348 = 0
Solve this to get the value of x

Answer 2

x and 16-x
2x^2-(16-x)^2=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
16-x=6
2 numbers are 10,6