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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}

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}


 

Grade:12

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

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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