SOLUTION: Find the value of X and Y from the given equation : sqrt(X)+Y=7 & sqrt(Y)+X=11

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Question 859033: Find the value of X and Y from the given equation : sqrt(X)+Y=7 & sqrt(Y)+X=11
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution, u=sqrt%28x%29, u%5E2=x, v=sqrt%28y%29,v%5E2=y
1.u%2Bv%5E2=7
2.v%2Bu%5E2=11
From eq. 1,
u=7-u%5E2
u%5E2=49-14v%5E2%2Bv%5E4
Substitute into eq. 2,
v%2B49-14v%5E2%2Bv%5E4=11
v%5E4-14v%5E2%2Bv%2B38=0
%28v-2%29%28v%5E3%2B2v%5E2-10v-19%29=0
Unfortunately the cubic cannot be factored any further.
You need to use numerical methods to find the roots.
v=-3.28
v=-1.85
v=3.13
and from above
v=2
We need to verify that each of these are actual solutions.
sqrt%28y%29=2
y=4
and
sqrt%28x%29%2B4=7
sqrt%28x%29=3
x=9
Verifying,
x%2Bsqrt%28y%29=11
9%2Bsqrt%284%29=11
9%2B2=11
11=11
True, good solution is x=9, y=4
Next,
v=3.13
sqrt%28y%29=3.13
y=9.797
sqrt%28x%29%2B9.797=7
sqrt%28x%29=-2.797
Doesn't lead to a valid solution.
Same for the other two possible solutions.
Only one solution.