SOLUTION: Given that x-y= 8•sqrt(2) and xy= 137, where x and y are both positive, find the value of x+y without finding x or y

Algebra ->  Equations -> SOLUTION: Given that x-y= 8•sqrt(2) and xy= 137, where x and y are both positive, find the value of x+y without finding x or y       Log On


   

Question 1139332: Given that x-y= 8•sqrt(2) and xy= 137, where x and y are both positive, find the value of x+y without finding x or y
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
The idea is to express  (x+y)^2  via given data, and then take square root of this expression (of this number).

It will be exactly (x+y).


So,


%28x+%2B+y%29%5E2 = %28x-y%29%5E2 + 4xy = %288%2Asqrt%282%29%29%5E2 + 4*137 = 64*2 + 4*137 = 676.


Therefore, (x+y) = sqrt%28676%29 = 26.


ANSWER.  x + y = 26.

Answered and solved.


Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Given:
(1) x-y+=+8%2Asqrt%282%29
(2) xy+=+137

Square equation (1):
x%5E2-2xy%2By%5E2+=+64%2A2+=+128

Add 4 times equation (2):
%28x%5E2-2xy%2By%5E2%29%2B4%28xy%29+=+128%2B4%28137%29+=+128%2B548+=+676
x%5E2%2B2xy%2By%5E2+=+%28x%2By%29%5E2+=+676
x%2By+=+sqrt%28676%29+=+26