SOLUTION: Solve the system algebraically by the substitution method: y= (x+1)^3 y= sq rt of (x-1)

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Question 356552: Solve the system algebraically by the substitution method:
y= (x+1)^3
y= sq rt of (x-1)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28300%2C300%2C-2%2C10%2C-2%2C10%2C%28x%2B1%29%5E3%2Csqrt%28x-1%29%29
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As you can see graphically, there is no solution (the curves never meet).
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Since both expressions equal y set them equal to each other.
%28x%2B1%29%5E3=sqrt%28x-1%29
Use a substitution,
Let u=x%2B1, u-2=x-1
%28x%2B1%29%5E3=sqrt%28x-1%29
u%5E3=sqrt%28u-2%29
u%5E6=u-2
u%5E6-u%2B2=0
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graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E6-x%2B2%29
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As you can see there is no real solution for u.
All 6 solutions are complex.
So then all 6 solutions for x will also be complex.
There are no real solutions.