The difference between two positive numbers is 10. Find the numbers, if the square of the greater exceds twice the square of the smaller by the maximum amount. {Answer--20,10}

Hi Shaleen,

Here x-y = 10

And we need to maximise x^2 - 2y^2.

So we need to maximise x^2 - 2(x-10)^2 = 40x - x^2 - 200 = 200 - (20-x)^2 --------{this is clearly max when x=20)

So x=20 and y=10, and that is the answer.

Hope that helps.

Best Regards,

Ashwin (IIT Madraa).

Approved