Math Problem Statement

solve 0=(4x^3)-8x

Solution

We are asked to solve the equation:

0=4x38x0 = 4x^3 - 8x

Step 1: Factor the equation

We can factor out the greatest common factor, which is 4x4x:

0=4x(x22)0 = 4x(x^2 - 2)

Step 2: Set each factor to zero

Now, set each factor equal to zero:

  1. 4x=04x = 0
  2. x22=0x^2 - 2 = 0

Step 3: Solve each equation

  1. 4x=04x = 0 implies x=0x = 0.
  2. x22=0x^2 - 2 = 0 implies x2=2x^2 = 2, so x=±2x = \pm \sqrt{2}.

Final Solution:

The solutions are:

x=0,x=2,x=2x = 0, \, x = \sqrt{2}, \, x = -\sqrt{2}

Would you like a more detailed explanation of any step?

Here are 5 related questions:

  1. How do you factor more complex cubic equations?
  2. What is the general method for solving quadratic equations?
  3. Can we apply the quadratic formula to solve x22=0x^2 - 2 = 0?
  4. What are the differences between real and complex roots in equations?
  5. How do you graph the function 4x38x4x^3 - 8x and find its roots?

Tip: When solving polynomial equations, always check if factoring can simplify the process before trying other methods like the quadratic formula.

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Math Problem Analysis

Mathematical Concepts

Algebra
Cubic Equations
Factoring

Formulas

Factoring method
Quadratic equation formula

Theorems

Fundamental Theorem of Algebra

Suitable Grade Level

Grades 9-12