Hi!

How should one proceed with an equation like this..

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

without having any calculator obv..

thanks!

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- Mar 23rd 2008, 11:32 AMTwigUnusual equation
Hi!

How should one proceed with an equation like this..

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

without having any calculator obv..

thanks! - Mar 23rd 2008, 11:43 AMbobak
let $\displaystyle y = x^{\frac{1}{4}}$

your equation becomes

$\displaystyle y^2 + y - 20 = 0$

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

can you take it form here? - Mar 23rd 2008, 01:10 PMTwighi
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.. - Mar 23rd 2008, 01:44 PMPlato
Because $\displaystyle x^{\frac{1}{4}} = - 5$ is impossible the there is one solution.

$\displaystyle x^{\frac{1}{4}} = 4\quad \Rightarrow \quad x = 64$ - Mar 23rd 2008, 03:26 PMTwighi
doesnt x = 256 ?

because 4^4 is 256

and sqrt of 256 is 16, so 16 plus 4 = 20 - Mar 23rd 2008, 03:30 PMmr fantastic
- Mar 24th 2008, 02:45 AMTwighi
Absolutely, the method is def. the most important.

Just wanted to be sure that I got it correct.

Thanks!