Question

How do I solve 0=-2/3x^(-5/3)+8/3x^(-2/3)?

Answer 1

Answer: The solution of the given equation is $\frac{1}{4}$.

Explanation:

The given equation is,

$\frac{2}{3}x^{ -\frac{5}{3}} +\frac{8}{3}x^{ -\frac{2}{3}}=0$

It can be written as,

$\frac{2}{3x^{ \frac{5}{3}}} +\frac{8}{3x^{ \frac{2}{3}}}=0$

$\frac{8x^{\frac{5}{3}}-2x^{\frac{2}{3}}}{3x^{\frac{7}{3}}}=0$

$8x^{\frac{5}{3}}-2x^{\frac{2}{3}}=0$

$2x^{\frac{2}{3}}(4x-1)=0$

Equate each factor equal to 0. Then we get,

$x=0$ and $\frac{1}{4}$

Since the power of x is in negative, so the equation is not defined for x = 0.

Therefore the only solution of the given equation is $\frac{1}{4}$.