SOLUTION: I would really appreciate your help. I have to solve these equations. a. index 3 (radicand 2x + 1) = 1 b. (radicand x + 2) = x -3 c. x ^ 1/3 = 3 = 0 Thank you so much

Algebra ->  Rational-functions -> SOLUTION: I would really appreciate your help. I have to solve these equations. a. index 3 (radicand 2x + 1) = 1 b. (radicand x + 2) = x -3 c. x ^ 1/3 = 3 = 0 Thank you so much      Log On


   

Question 546018: I would really appreciate your help.
I have to solve these equations.
a. index 3 (radicand 2x + 1) = 1
b. (radicand x + 2) = x -3
c. x ^ 1/3 = 3 = 0
Thank you so much
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a. index 3 (radicand 2x + 1) = 1
I think you mean
root%283%2C%282x+%2B+1%29%29+=+1
2x + 1 = 1
x = 0
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b. (radicand x + 2) = x -3
sqrt%28x%2B2%29+=+x-3
x%2B2+=+x%5E2+-+6x+%2B+9
x%5E2+-+7x+%2B+7+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-7x%2B7+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-7%29%5E2-4%2A1%2A7=21.

Discriminant d=21 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+21+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+21+%29%29%2F2%5C1+=+5.79128784747792
x%5B2%5D+=+%28-%28-7%29-sqrt%28+21+%29%29%2F2%5C1+=+1.20871215252208

Quadratic expression 1x%5E2%2B-7x%2B7 can be factored:
1x%5E2%2B-7x%2B7+=+%28x-5.79128784747792%29%2A%28x-1.20871215252208%29
Again, the answer is: 5.79128784747792, 1.20871215252208. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B7+%29

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c. x ^ 1/3 = 3 = 0
too many equal signs.