Question 1104242: Find the product (xy) if x+y+ = 20 and x-y+ =12.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
It is assumed in the given equations that  >= 0 and  >= 0.
1. Let u =  . Then
 = 20, or
 = 0.
Factor left side
(u+5)*(u-4) = 0.
As just noticed above, assumed to be >= 0.
Therefore, only positive root u = 4 works.
Thus, = 4. Then x + y = 4^2 = 16.
2. Similarly, Let v =  . Then
 = 12, or
 = 0.
Factor left side
(v+4)*(v-3) = 0.
As just noticed above, assumed to be >= 0.
Therefore, only positive root v = 3 works.
Thus, = 3. Then x - y = 3^2 = 9.
3. Thus we have two equations
x + y = 16,
x - y = 9,
which implies x= 12.5, y= 3.5.
Answer. The solution is x= 12.5, y= 3.5. The product xy = 43.75.
Solved.
Answer by greenestamps(13209)  (Show Source):
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