Question

solve $x^3 = 125$, where $x$ is a real number.
simplify your answer as much as possible.

if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.

$x = -5, 5$

Explanation:

Step1: Recall the cube root property

For the equation \(x^3 = a\), the real - number solution is \(x=\sqrt[3]{a}\) because the cube function \(y = x^3\) is a one - to - one function (it passes the horizontal line test), meaning that for every real number \(y\), there is exactly one real number \(x\) such that \(y=x^3\).

Step2: Calculate the cube root of 125

We know that \(5\times5\times5 = 5^3=125\) and \((- 5)\times(-5)\times(-5)=- 125
eq125\). So, to solve \(x^3 = 125\), we take the cube root of both sides: \(x=\sqrt[3]{125}\). Since \(5^3 = 125\), we have \(x = 5\). The previous answer of \(x=-5,5\) is incorrect because \((-5)^3=-125
eq125\).

Answer:

\(x = 5\)