Question

how to solve this equation?
4x^(1/3)=2x^(-2/3)

Answer 1

Solve for x over the real numbers:
4 x^(1/3) = 2/x^(2/3)
Move everything to the left hand side.
Subtract 2/x^(2/3) from both sides:
4 x^(1/3)-2/x^(2/3) = 0
Simplify 4 x^(1/3)-2/x^(2/3) = 0 by making a substitution.
Simplify and substitute y = x^(1/3): 4 x^(1/3)-2/x^(2/3) = 4 x^(1/3)-(2)/(x^(1/3))^2 = 4 y-2/y^2 = 0:
4 y-2/y^2 = 0
Write the left hand side as a single fraction.
Bring 4 y-2/y^2 together using the common denominator y^2:
(2 (2 y^3-1))/y^2 = 0
Divide both sides by a constant to simplify the equation.
Divide both sides by 2:
(2 y^3-1)/y^2 = 0
Multiply both sides by a polynomial to clear fractions.
Multiply both sides by y^2:
2 y^3-1 = 0
Isolate terms with y to the left hand side.
Add 1 to both sides:
2 y^3 = 1
Divide both sides by a constant to simplify the equation.
Divide both sides by 2:
y^3 = 1/2
Elminate the power on the left hand side.
Take cube roots of both sides:
y = 1/2^(1/3)
Perform back substitution on y = 1/2^(1/3).
Substitute back for y = x^(1/3):
x^(1/3) = 1/2^(1/3)
Eliminate the cube root on the left hand side.
Raise both sides to the power of three:
Answer: |
| x = 1/2

Answer 2

I hope that's something correct.

Answer 3

sorry, i don;t get it. it looks too messy ` could you please use Equation?

Answer 4

Is x = 1/2 even remotely the answer?

Answer 5

yes the answer is 1/2, but i need detail,

Answer 6

could you please use Equation?

Answer 7

Solve for x over the real numbers:
4 x^(1/3) = 2/x^(2/3)

Subtract 2/x^(2/3) from both sides:
4 x^(1/3)-2/x^(2/3) = 0

Simplify and substitute y = x^(1/3): 4 x^(1/3)-2/x^(2/3) = 4 x^(1/3)-(2)/(x^(1/3))^2 = 4 y-2/y^2 = 0:
4 y-2/y^2 = 0

Bring 4 y-2/y^2 together using the common denominator y^2:
(2 (2 y^3-1))/y^2 = 0

Divide both sides by 2:
(2 y^3-1)/y^2 = 0

Multiply both sides by y^2:
2 y^3-1 = 0

Add 1 to both sides:
2 y^3 = 1

Divide both sides by 2:
y^3 = 1/2

Take cube roots of both sides:
y = 1/2^(1/3)

Substitute back for y = x^(1/3):
x^(1/3) = 1/2^(1/3)

Raise both sides to the power of three:

Answer: |
| x = 1/2

Answer 8

x^(1/3): 4 x^(1/3)-2/x^(2/3) = 4 x^(1/3)-(2)/(x^(1/3))^2 = 4 y-2/y^2 = 0:

Answer 9

dont get that part

Answer 10

Here's a simpler way: