Math Problem Statement
Solution
The equation shown is:
To solve this equation for , let's go through it step-by-step.
-
Rewrite the Equation: Move the second term to the other side:
-
Clear the Denominator: Multiply both sides by (assuming ) to eliminate the fraction:
-
Isolate : Divide both sides by 4:
-
Solve for : Take the sixth root of both sides. Since we are dealing with a real number solution, we have:
-
Simplify:
Thus, the solutions are:
Would you like further details on any of these steps?
Here are some related questions you might explore:
- How can we generalize this approach to equations involving higher powers?
- What if the equation had a different constant instead of 4?
- Can we solve similar equations by taking logarithms?
- How would complex solutions differ in this problem?
- What is the significance of rational exponents when solving polynomial equations?
Tip: When dealing with equations with fractions, clearing the denominator early on can simplify the problem.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Rational Equations
Exponents
Formulas
\( \frac{1}{x^2} = 4x^4 \)
Isolating terms by clearing denominators
Solving equations involving fractional exponents
Theorems
Properties of Exponents
Square and Cube Roots
Suitable Grade Level
Grades 10-12
Related Recommendation
Solving Equation with Rational Expressions: \(\frac{1}{x^2} - 4 \cdot \frac{1}{x^4} = 0\)
Solving Rational Exponential Equation 1/x^2 - 4x^(1/4) = 0
Solving Fractional Exponent Equation: (2x^(1/2)) - (x^(1/4)) = 0
Solving Equations with Fractional Exponents: x^(1/2) - 4x^(1/4) = 0
Solving Rational and Cubic Equations: Real Solutions to \(\frac{1}{2x^2} - 9x^4 + 5 = 0\)