Unusual equation

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March 23rd 2008, 11:32 AM
Twig

Unusual equation

Hi!

How should one proceed with an equation like this..

x^(1/2) + x^(1/4) = 20

without having any calculator obv..

thanks!
March 23rd 2008, 11:43 AM
bobak

let $y = x^{\frac{1}{4}}$

your equation becomes

$y^2 + y - 20 = 0$

factor $(y+5)(y-4)=0$

can you take it form here?
March 23rd 2008, 01:10 PM
Twig

hi

uh..
I understood what you did.

y = -5 or y = 4 ?

but.. do I get the correct answer?
If I insert 4 into the original equation..
March 23rd 2008, 01:44 PM
Plato

Because $x^{\frac{1}{4}} = - 5$ is impossible the there is one solution.
$x^{\frac{1}{4}} = 4\quad \Rightarrow \quad x = 64$
March 23rd 2008, 03:26 PM
Twig

hi

doesnt x = 256 ?

because 4^4 is 256

and sqrt of 256 is 16, so 16 plus 4 = 20
March 23rd 2008, 03:30 PM
mr fantastic

Quote:

Originally Posted by Twig

doesnt x = 256 ?

because 4^4 is 256

and sqrt of 256 is 16, so 16 plus 4 = 20

Yes.

Plato made a simple careless mistake. Be that as it may, it's a mere detail - it's the method that's important and the method is what Plato's given you.
March 24th 2008, 02:45 AM
Twig

hi

Absolutely, the method is def. the most important.
Just wanted to be sure that I got it correct.

Thanks!

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