# Re: Some Silly Problems...

AbhyX said:

> 11. X^(1/3) - X^(1/9) = 60
> Solve for X.

In solving such problems, it is often helpful to substitute a temporary
variable which simplifies the expression.

We note that (X^(1/9))^3 is X^(1/3), and set Y = X^(1/9). Thus, we are
trying to solve: Y^3 - Y = 60.

Because we are fairly familiar with the cubes up to about 5 or so, we can
easily see that 4^3 is 64. So that tells us straight away that Y = 4.

Thus, X^(1/9) = 4.

X is therefore 4^9, or 262144.

I suggest you invest in an elementary mathematics textbook. :-)

--
Richard Heathfield
"Usenet is a strange place" - dmr 29/7/2005
http://www.cpax.org.uk
email: rjh at above domain (but drop the www, obviously)
.

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