SOLUTION: solve the following system of equations: x + y + square root(xy) = 28 x^2 + y^2 + xy = 336

Question 348952: solve the following system of equations:
x + y + square root(xy) = 28
x^2 + y^2 + xy = 336
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
solve the following system of equations:
x + y + = 28
x^2 + y^2 + xy = 336
:
Simplify the 1st equation to use for elimination
x + y =
square both sides
=
subtract xy from both sides
=
=
:
Use for elimination with 2nd equation
=

---------------------------Subtraction eliminates everything on the left, we have:

divide both sides by 56, results:

square both sides
xy = 64
y =
:
Substitute for y in the 1st equation
x + y + = 28
x + + = 28
x's inside the radical cancel
x + + = 28
x + + 8 = 28
x + = 28 - 8
x + = 20
multiply by x
x^2 + 64 = 20x
A quadratic equation
x^2 - 20x + 64 = 0
Factors to
(x-16)(x-4)
x = 16
x = 4
:
Find y:
When x=16: y = 64/16 = 4
When x=4: y = 64/4 = 16
:
:
Check solution in the 1st equation
16 + 4 + = 28
20 + = 28; confirms our solutions; x=16, y-4 and x=4, y=16
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