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

Question

asked Dec 13, 2019 23.0k views

1 Answer

Meny · Answer 1 · 2019-12-20T02:25:06+0000

Answer: The solution of the given equation is
(1)/(4) .

Step-by-step explanation:

The given equation is,

$(2)/(3)x^{ -(5)/(3)} +(8)/(3)x^{ -(2)/(3)}=0$

It can be written as,

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

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

$8x^{(5)/(3)}-2x^{(2)/(3)}=0$

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

Equate each factor equal to 0. Then we get,

x=0 and
(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
(1)/(4) .