What is the largest possible value of x given that x^3 = 5x? Express your answer in simplest radical form.

Question

What is the largest possible value of x given that
`x^3 = 5x`? Express your answer in simplest radical form.

Answer 1

x^3 = 5x

Subtract 5x from both sides:

x^3 - 5x = 0

Factor X out of x^3:

x(x^2-5x) = 0

Set X to 0 and solve for x:

x = 0

Set (X^2-5) to equal 0 and solve for x:

x^2 - 5 = 0

Add 5 to both sides:

x^2 = 5

Take the square root of both sides:

x = √5, -√5

The three solutions of x are 0, √5, -√5

In order from smallest to largest = -√5, 0, √5

The largest possible value is √5