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

Explanation

Let larger part be x. Then, the smaller part =16-x
Accroding to given statement
`2x^(2)-(16-x)^(2)=164`
`implies2x^(2)-(256+x^(2)-32x)=164`
`implies2x^(2)-256-x^(2)+32x-164=0`
`impliesx^(2)+32x-420=0`
`impliesx^(2)+42x-10x-420=0`
`impliesx(x+42)-10(x+42)=0`
`implies(x+42)(x-10)=0`
`impliesx=-42orx=10`
`impliesx=10" "(":'x=-42 ""is not possible")`
Hence, the equired parts are 10 and 6.