SOLUTION: (x+y)^2 + (x+3y)^2 - 10(x+3y) - 4(x+y) +29 = 0 , find the value from next expresion 2y^2 + xy

Question 42466:
(x+y)^2 + (x+3y)^2 - 10(x+3y) - 4(x+y) +29 = 0 , find the value from next expresion

2y^2 + xy
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!

This looks like a neat problem. Let's rearrange it and see if this helps sort it out, and subtract 29 from each side while you are at it:

Notice that you can "complete the square" (remember "half and square"??) on each of these quantities, by adding 4 on the first blank and 25 on the second blank.

Since the sum of two squares equals zero, this means that each quantity squared must equal zero!

x+y-2=0 and x+3y-5=0

x+y=2
x+3y=5

Solve by elimination:
-x-y=-2
x+3y=5

So, 2y = 3,

x+y=2

NOW, you wanted 2y^2 + xy=

It might have been easier to just multiply out the quantities involved and hope for an easy solution to this!

Nope!! That's not going anywhere that I can see!! Better stick to my first solution. I don't know how to check it. You'll have to check it for me!! I never was any good at math!!!

R^2 at SCC
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