Question #9c8b1

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Answer 1 · 2017-03-16T20:23:44

#x=+-oo

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

Tony B