Question

Find the exact solution of x. 4x^3 = 500

Answer 1

$4x^3=500\\ x^3=125\\ x=5$

Answer 2

Answer:  The required exact solution is x = 5.

Step-by-step explanation:  We are to find the exact solution of the following cubic equation for x :

$4x^3=500~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

To solve the given equation, first we will make the coefficient of x³ as 1 and then we will take the cube root on both sides.

From equation (i), we have

$4x^3=500\\\\\Rightarrow x^3=\dfrac{500}{4}\\\\\Rightarrow x^3=125\\\\\Rightarrow x=\sqrt[3]{125}\\\\\Rightarrow x=5.$

Thus, the required exact solution is x = 5.