Troubleshooting Inverse Functions: Solving Algebraic Problems

[aquitaine]

Ok, I decided to review basic algebra since I haven't done anything with it in like, forever. I came across an inverse function problem that I can't get the right answer.

the equation is:

y = cuberoot(x+sqrt(1+x^2)) + cuberoot(x-sqrt(1+x^2))

I tried replacing X with Y, and solving for Y
and getting rid of the cube roots by cubing both sides
X^3 = y + sqrt(1+y^2) + y - sqrt(1+y^2)
simplifying a bit (the square roots go away)
x^3 = 2y
so
y = (1/2)x^3

Yet the book I'm using says the answer is y=(1/2)(3x+x^3)

What did I do wrong?

 

[Shooting Star]

(a+b)³ =/= a³ + b³, as you have done.

Use (a+b)³ = a³ + b³ +3ab(a+b).

Start with y = a+b, and cube both sides. If you put a+b=y again, the result comes quickly,

 

[aquitaine]

thanks, I think I got it. Man, a few years ago I could have done this, but now? I feel like a 9th grader again.