SOLUTION: {{{x^(1/2)+y=7}}} {{{x+y^(1/2)=11}}} solve this equations for x and y

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Question 7773: x%5E%281%2F2%29%2By=7
x%2By%5E%281%2F2%29=11
solve this equations for x and y
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
To solve:
x%5E%281%2F2%29%2By=7 ...(1)
x%2By%5E%281%2F2%29=11 ...(2)
From(1): x^(1/2) = 7 - y ,
Squaring both sides:
x = (7-y)^2 = y^2 - 14y + 49,
Goto (2): y^2 - 14y + 49 + y^(1/2) = 11,
Let w = y^1/2, so y = w^2,
so we have w^4 - 14 w^2 + w + 38 = 0,
Use syntheic division,we have
1 + 0-14 + 1 + 38 (2
+ 2 +4 -20 -38
----------------------
1 + 2 -10 -19 + 0
Hence,(w-2)(w^3 + 2w^2-10w -19) = 0.
Unfortunately, we cannot factor w^3 + 2w^2-10w -19,
and the three roots are in very bad form.

Note,when w =2, y= 4 and x = 16 - 56 + 49 = 9
So, here I only give you one set of solution
x= 9 and y = 4.
Kenny