SOLVED Quadratic equations problem

Jul 2010
461
25
Hi all,

Can any one confirm that I am not losing it on these 2 problems!?
Solve for x,
\(\displaystyle t=-6x^2+6x\)

I calculate \(\displaystyle x=\frac{-6\pm \sqrt{36-24t}}{-12}\) which i knw can be further reduced but the answer in the book is \(\displaystyle x=3\pm \sqrt{9-t}\) and

\(\displaystyle t=\frac{x^2}{2} + \frac{9}{2}-2x\)

I calculate \(\displaystyle x=\frac{4\pm \sqrt{-20+8t}}{2}\) but the answer in the book is \(\displaystyle x=2 \pm\sqrt{2t-5}\)

thanks
 
Dec 2009
3,120
1,342
Hi all,

Can any one confirm that I am not losing it on these 2 problems!?

1. Solve for x,

\(\displaystyle t=-6x^2+6x\)

I calculate \(\displaystyle x=\frac{-6\pm \sqrt{36-24t}}{-12}\) which i know can be further reduced, but the answer in the book is \(\displaystyle x=3\pm \sqrt{9-t}\)

The book solution is the answer to...... \(\displaystyle t=-x^2+6x\)


and 2.

\(\displaystyle t=\frac{x^2}{2} + \frac{9}{2}-2x\)

I calculate \(\displaystyle x=\frac{4\pm \sqrt{-20+8t}}{2}\) but the answer in the book is \(\displaystyle x=2 \pm\sqrt{2t-5}\)

Just continue to simplify

thanks
\(\displaystyle \frac{4\pm\sqrt{-20+8t}}{2}=\frac{4}{2}\pm\frac{\sqrt{8t-20}}{\sqrt{4}}=2\pm\sqrt{\frac{8t-20}{4}}\)
 
Jul 2010
461
25
ah, so simple (Doh)
i may start thinking outside the box!!!

thanks archie!