SOLUTION: I need to solve this equation algebraically sqrt (x+1)= cube root (4x-4)

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Question 430024: I need to solve this equation algebraically
sqrt (x+1)= cube root (4x-4)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt%28x%2B1%29+=+root%283%2C4x-4%29+Raise each sides to the 6th power
+%28sqrt%28x+%2B+1%29%29%5E6+=+%28root%283%2C4x-4%29%29%5E6+
+%28x+%2B+1%29%5E3+=+%284x-4%29%5E2+
+x%5E3+%2B+3x%5E2+%2B+3x+%2B+1+=+16x%5E2+-+32x+%2B+16+
+x%5E3+-+13x%5E2+%2B+35x+-+15+=+0+
This has me stumped.
I can say +%28+x+-+b+%29%2A%28+x%5E2+%2B+a+%29+=+x%5E3+-+b%2Ax%5E2+%2B+ax+-+a%2Ab+=+0+
I can say
a+=+35
b+=+13
a%2Ab+=+455
I'll rewrite the equation
+x%5E3+-+13x%5E2+%2B+35x+=+15+
Add 455 to both sides
+x%5E3+-+13x%5E2+%2B+35x+%2B+455+=+470+
+%28+x+-+13+%29%2A%28+x%5E2+%2B+35+%29+=+470+
Looking at this, the answer seems to be between
14 and 15. Maybe you can find a
cubic equation solver on the internet.