HW Question Factoring

**civiliam** · October 2nd 2008, 08:33 AM

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...

**Sean12345** · October 2nd 2008, 08:50 AM

Hi civiliam,

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

Hope this helps.

**civiliam** · October 2nd 2008, 08:56 AM

thank you so much that's perfect

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