SOLUTION: If x + y is equals to 4 find maximum or minimum possible value of x square + y square

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Question 1207563: If x + y is equals to 4 find maximum or minimum
possible value of x square + y square
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39616) About Me  (Show Source):
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Let V = the value that we want to maximize or minimize

V%22%22=%22%22x%5E2%2By%5E2, where x%2By%22%22=%22%224 or y=4-x

V%22%22=%22%22x%5E2%2B%284-x%29%5E2

V%22%22=%22%22x%5E2%2B%2816-8x%2Bx%5E2%29

V%22%22=%22%222x%5E2-8x%2B16%29

That is a parabola opening upward, so it has a minimum value but no maximum
value.

Use the vertex formula to find the x-coordinate of the minimum point:

-b%2F%282a%29%22%22=%22%22-%28-8%29%2F%282%2A2%29=2

Substituting in 

V%5Bmin%5D%22%22=%22%222%282%29%5E2-8%282%29%2B16%298

So the minimum value is 8, which occurs when x=2, and y = 4-x = 4-2 = 2.

Edwin