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 2 years ago
What are the max and min possible values of x2 + y 2 if x+y =1 and x and y are nonnegative? What inequality between x2 + y 2 and (x+y)2 does this yield that holds for arbitrary nonnegative numbers x and y?
 2 years ago
What are the max and min possible values of x2 + y 2 if x+y =1 and x and y are nonnegative? What inequality between x2 + y 2 and (x+y)2 does this yield that holds for arbitrary nonnegative numbers x and y?

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Jonask
 2 years ago
Best ResponseYou've already chosen the best response.0\[(1)^2=x^2+2xy+y^2\] \[x^2+y^2=12xy\] min

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.0\[2y2x=0\] \[x=y\] max 1/2 min ?

Stacey
 2 years ago
Best ResponseYou've already chosen the best response.0Because x+y=1 and the variables cannot be negative \[0 \le x \le1\]\[0 \le y \le1\]Also y=1x, so \[y^{2}=(1x)^{2}=12x+x ^{2}\]Substitute that into your first equation to obtain \[12x+2x ^{2}\]Graphing this with the domain or using the derivative, you should be able to find the max and min.
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