Question

The difference between two +ve numbers is 10. If the difference between the square of the greater and twice the square of the smaller is maximum then the numbers are

• A. 20,10
• B. 10, 20
• C. 30, 20
• D. 20, 30

Answer 1

Answer: (A)

20,10

$x-y=10$
$x^2-2y^2$ maximize it
$f\left(x\right)=x^2-2(x-10{)}^2$
$f^{\prime }\left(x\right)=2x-4(x-10)$
$2x=40$
$x=20$ $y=10$