Question

divide 16 into two parts such that 2 times the square of larger part is 164 more than the square of smaller part

Answer 1

Hey

Here is your answer,

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
x2 – 58x – 6x + 348 = 0
x(x – 58) – 6(x – 58) = 0
(x – 58)(x – 6) = 0
(x -58) = 0 or (x – 6) = 0
Therefore, x = 58 or 6
x ≠ 58 (since the number itself is 16)
Thus x = 6
16 – x = 16 – 6 = 10

Hope it helps you!