Question

Question #9c8b1

Answer 1

#x=+-oo

Explanation:

Given:`" "2/3x^(-2/3)=0`

Multiply both sides by 3/2

`x^(-2/3)=0`

THERE IS A TRAP IN THIS!!!!

It is tempting to say that `x=0` This is wrong!

`x^(-2/3)" is the same as " 1/(x^(2/3))`

Clearly `x!=0` as this is an excluded value in that `1/0` is 'not allowed'. However as `x->0` then `x^(2/3)->0" "` so `" "1/(x^(2/3))->oo`

So lets consider the other end of the 'number spectrum' instead of x=0 what about `x=oo`

In this condition we end up with `1/(x^(2/3)->oo)` which is so minute that it may as well be 0, but in this case it exists

So `2/3x^(-2/3)=0" "=>" "x=+-oo`