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# algebra

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Let x and y be real numbers such that 2(x^2 + y^2) = x + y + 8.  Find the maximum value of x - y.

May 22, 2021

#1
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The maximum value of x - y is 3*sqrt(2).

May 22, 2021
#2
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The above is the graph of

I used Winplot to plot the two functions and find their extreme values. You could also use calculus to do the same , and if requested, I would be happy to show my work.

But where does the equation come from? The equation given is the equation of a circle that has the standard form

I solved this equation for y to get

and then subtracted the expression for y from x to get f(x). By the way, the exact values of the coordinates of the extreme point displayed in the plot are

So the maximum value of x-y is $$\frac{\sqrt{33}}{2}$$ or approximately 2.87228.

May 23, 2021