Question

The difference between two positive numbers is 10. Find the numbers, if the square of the greater exceeds twice the square of the smaller by the maximum amountThe difference between two positive numbers is 10. Find the numbers, if the square of the greater exceeds twice the square of the smaller by the maximum amount

Answer 1

The Numbers are 20 and 10

Step-by-step explanation:

If one number is x then the other number will be x-10

Now, according to the question difference between the square of the greater and twice the square of the smaller number

$x^2-2(x-10)^2$

$=x^2-2(x^2-20x+100)$

$=x^2-2x^2+40x-200$

$=-x^2+40x-200$

$=-200-(x^2-40x+400)+400$

$=200-(x-20)^2$

This value will be maximum when x=20

Thus, the numbers are 20 and 10

Hope this answer is helpful.

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