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r = a*sqrt(b^2-c^2) What does b equal to?

Quote: Originally Posted by the undertaker r = a*sqrt(b^2-c^2) What does b equal to? $\displaystyle r=a(\sqrt{b^2-c^2})$ $\displaystyle r^2=a^2(b^2-c^2)$ $\displaystyle \frac{r^2}{a^2} = b^2 - c^2 $ $\displaystyle \frac{r^2}{a^2} + c^2 = b^2 $ $\displaystyle b=\sqrt{ \frac{r^2}{a^2} - c^2}$ that what you mean

Quote: Originally Posted by Amer $\displaystyle \frac{r^2}{a^2} + c^2 = b^2 $ $\displaystyle b=\sqrt{ \frac{r^2}{a^2} - c^2}$ No, the last line should read $\displaystyle \sqrt{b^2}=\sqrt{ \frac{r^2}{a^2} + c^2}$ and as $\displaystyle \sqrt{b^2}=|b|$, there are two solutions : $\displaystyle \pm\sqrt{ \frac{r^2}{a^2} + c^2}$.