I don't know how to go on about solving this...

IT asks Use factoring to solve the equation for the real values of the variable

y^4 - 26y^2 + 25 = 0

I know how to factor but this one is throwing me off...

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- Oct 2nd 2008, 08:33 AMciviliamHW Question Factoring
I don't know how to go on about solving this...

IT asks Use factoring to solve the equation for the real values of the variable

y^4 - 26y^2 + 25 = 0

I know how to factor but this one is throwing me off... - Oct 2nd 2008, 08:50 AMSean12345
Hi civiliam,

We have $\displaystyle y^4-26y^2+25=0$ . Notice that this is a quadratic in $\displaystyle y^2$ , thus if we let $\displaystyle w=y^2$ we can re-write the equation as $\displaystyle w^2-26w+25=0$ . Now this is a fairly routine quadratic since $\displaystyle w^2-26w+25=(w-25)(w-1)=0$ and thus we can conclude that $\displaystyle w=25$ , $\displaystyle w=1$ . Since $\displaystyle w=y^2$ we can say $\displaystyle y^2=25$ , $\displaystyle y^2=1$ and therefore the four roots of the equation are $\displaystyle \pm 5$ , $\displaystyle \pm 1$ .

Hope this helps. - Oct 2nd 2008, 08:56 AMciviliam
thank you so much that's perfect