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...
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.