- #1
Spiralshell
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Homework Statement
SOLVE: √(X)-3√(X-1)=1
//That is SQRT(X)-CBRT(X-1)=1; where SQRT = Square root, and CBRT = Cube root.
Homework Equations
None that I know of...
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...
Homework Statement
9x-2(3x+1)+9=0
Homework Equations
None that I know of...
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.
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