1. The problem statement, all variables and given/known data SOLVE: √(X)-3√(X-1)=1 //That is SQRT(X)-CBRT(X-1)=1; where SQRT = Square root, and CBRT = Cube root. 2. Relevant equations None that I know of... 3. The attempt at a solution (I would like to note I have no idea whether I am even approaching this problem the correct way.) √(X)-3√(X-1)=1 (√(X) - 3√(X-1))3=13 (√(X)-3√(X-1))((√(X)-3√(X-1))((√(X)-3√(X-1)) Now I foil the first two right? Then leave the 3rd and do the sum of cubes? I don't know what happens when you multiply a square root to a cube, I imagine it is something like: e.g. SQRT(X) * CBRT(X) = X^(1/2) * X(1/3) = X^(1/6) which would be 6√X, but then what do I do? Also, my professor gave us the answers, but never showed us how to solve it. The answers are X=0, 1, and 9 (THIS IS NOT A GIVEN). I feel so lost and I can't find this anywhere in my precalculus book :(! Nothing even remotely similar... 1. The problem statement, all variables and given/known data 9x-2(3x+1)+9=0 2. Relevant equations None that I know of... 3. The attempt at a solution So, my professor showed us how to do this one, but I don't understand it at all... 9x=(32)x=(3x)2 //no idea what this is... 9x-2(3x+1)+9=0 3(x)2-6(3x)+9=0 //I don't understand how we get 3(x)2, remove X+1 for X LET Y=3x How do we decide this? Y2-6y+9=0 //I Understand it from here on.. I just need a lot of clarification to understand this stuff.