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=(500)/(4)\\\\\Rightarrow x^3=125\\\\\Rightarrow x=\sqrt[3]{125}\\\\\Rightarrow x=5.`

Thus, the required exact solution is x = 5.