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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).
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