So I got myself a question from the textbook for practice and I came across this question.
The difference between two positive numbers is 10. Find the numbers, if the square of greater number exceeds twice the square of the smaller by a maximum amount
This is what I could do
I took the numbers as x and y
So, x - y = 10 - i
Then the greatest number be Z.
Z = x^2 * y^2. - ii
But this didn’t give me the answer. What could be the second equation?
Btw latex isn’t supported in safari of my phone. Sorry.
You want $x-y=10$ and $x^2-2y^2$ is maximum.
That is, $x^2-2(10-x)^2=-x^2+40x-200$ is maximum.
A trinomial $ax^2+bx+c$ with $a<0$ has a maximum at $x=-\dfrac{b}{2a}$ (if you don't know it yet, prove it). Here that means the maximum occurs for $x=20$, hence $y=10$.