Here's one of the questions I have problems with:
cube root of (x+2)=6th root of (9x+10)
A. -1, 6
B. [-13 +/- sqrt(193)]/2
C. 1, -6
D. [13 +/- sqrt(145)]/2
Please explain how to solve this. Should you cube both sides, or raise both to the 6th? and I get lost trying to do more than square a radical. i'd show my "work" which is basically nonsense but it's useless because I honestly have no idea how to solve this.
thanks in advance for the help. having an example of how to solve these kinds of problems would help me a lot, so if you can step by step would be great.
I did it later above
To solve this equation, we need to isolate x. Here's how to approach it step by step:
Step 1: Start by rewriting the equation with each side raised to the 6th power.
[(x+2)^(1/3)]^6 = [(9x+10)^(1/6)]^6
Step 2: Simplify the equation.
(x+2)^(6/3) = (9x+10)^(6/6)
(x+2)^2 = 9x+10
Step 3: Expand the squared term.
x^2 + 4x + 4 = 9x + 10
Step 4: Rearrange the equation to have all terms on one side.
x^2 - 5x - 6 = 0
Step 5: Factorize or use the quadratic formula to solve for x.
(x - 6)(x + 1) = 0
Setting each factor to zero gives:
x - 6 = 0 --> x = 6
x + 1 = 0 --> x = -1
Step 6: Check the solutions.
Substitute the found solutions back into the original equation to check if they satisfy it. In this case, both x = 6 and x = -1 are valid solutions.
Therefore, the correct answer is A. -1, 6.