SOLUTION: xy=12, (x^2+y^2)=25 then what is the value of (x+y)2^2

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Question 1011843: xy=12, (x^2+y^2)=25 then what is the value of (x+y)2^2
Found 4 solutions by addingup, ikleyn, MathTherapy, Fombitz:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
(x^2+y^2)=25 take the square root on both sides:
x+y= 5
(x+y)2^2 and since x+y= 5:
5(2)^2= 5(4)= 20

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
xy=12, (x^2+y^2)=25 then what is the value of (x+y)2^2 ?
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xy=12, x%5E2%2By%5E2 = 25 implies that

x%5E2+%2B+2xy+%2B+y%5E2 = x%5E2%2By%5E2 + 2xy = 25 + 2*12 = 25 + 24 = 49.

Again:

%28x%2By%29%5E2 = x%5E2+%2B+2xy+%2B+y%5E2 = 49.

So, if you need %28x%2By%29%5E2, you just have it: it is 49.

What you do REALLY need, I don't know, because you do neglect to use parentheses properly.

If it is %28%28x%2By%29%2A2%29%5E2, then it is equal to 4*49.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
xy=12, (x^2+y^2)=25 then what is the value of (x+y)2^2
xy+=+12   ;   x%5E2+%2B+y%5E2+=+25

Observing x%5E2+%2B+y%5E2+=+25, it's obvious that x and y MUST be 3 and 4
Likewise x and y MUST be 3 and 4 as xy = 12
Proving this, we get:
%28x+%2B+y%29%5E2+=+x%5E2+%2B+2xy+%2B+y%5E2 --------> x%5E2+%2B+y%5E2+%2B+2xy, which becomes: 25 + 2(12) = 25 + 24 = 49
Since %28x+%2B+y%29%5E2+=+49, then x + y = 7 ------ Square root of each side was taken
I don’t know what %28x+%2B+y%292%5E2 means but you should be able to determine what’s needed since it was found that:
%28x+%2B+y%29%5E2+=+49 & x+%2B+y+=+7, and the following were given: xy+=+12 & %28x%5E2+%2B+y%5E2%29+=+25+

Answer by Fombitz(32388) About Me  (Show Source):