Can someone help me solve this and write the answer in simplified radical form?
(z - 5)^3 + 32 = 0
Oh, solve for "z"... obviously.
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z-5 = (-32)^(1/3)
z-5 = 8^1/3) (-4)^(1/3)
z = 5 - 2(4)^(1/3) or 5 - 2cuberoot(4)
Thanks!!!
But one other question, it's just 5 - 2 cuberoot(4)? That's the only answer? Or is it 5 - 2 cube(4) AND 5 + 2 cube(4)??? Sorry... just paranoid here.
No problem! It's always good to double-check to make sure you have the correct answer.
In this case, the equation (z - 5)^3 + 32 = 0 has only one real solution, which is z = 5 - 2∛4 or 5 - 2cuberoot(4). This is because the cube root (∛) of a number can be positive or negative, but the equation only has one solution.
So, the answer is indeed z = 5 - 2cuberoot(4). There is no need to consider the positive cube root as part of the solution in this case.
If there were more than one solution, it would be necessary to consider both the positive and negative cube roots. However, in this particular equation, there is only one solution.