My expression is -3=[(-x*pi)/(sqrt(1-x^2))]
An online equation solver gave a solution of x=3/[sqrt(9+pi^2)] or x=.690621 but does not show the working.
I have spent hours on this but am positively stuck!
Can anyone help?
Regards.
My expression is -3=[(-x*pi)/(sqrt(1-x^2))]
An online equation solver gave a solution of x=3/[sqrt(9+pi^2)] or x=.690621 but does not show the working.
I have spent hours on this but am positively stuck!
Can anyone help?
Regards.
$\displaystyle \displaystyle -3 = \frac{-x\times \pi}{\sqrt{1-x^2}}$
$\displaystyle \displaystyle -3 \sqrt{1-x^2}= -x\times \pi$
$\displaystyle \displaystyle 3 \sqrt{1-x^2}= x\times \pi$
$\displaystyle \displaystyle 3^2 (1-x^2)= x^2\times \pi^2$
$\displaystyle \displaystyle 9-9x^2= x^2\times \pi^2$
$\displaystyle \displaystyle 9-9x^2- \pi^2x^2=0 $
$\displaystyle \displaystyle 9-(9+ \pi^2)x^2 =0$
$\displaystyle \displaystyle (9+ \pi^2)x^2 =9$
$\displaystyle \displaystyle x^2 =\frac{9}{9+ \pi^2}$
$\displaystyle \displaystyle x =\sqrt{\frac{9}{9+ \pi^2}}$
Generally speaking, you can only simplify a radical expression that is in factored form.
$\displaystyle \sqrt{9x^2}$ for example CAN be simplified to $\displaystyle 3x$
The expression $\displaystyle \sqrt{x^2 + 9}$ on the other hand cannot be simplfied as-is.
This is especially apparent when you recall that $\displaystyle (a + b)^2 \neq a^2 + b^2$, because the square root would be the same as $\displaystyle (a + b)^{\frac{1}{2}}$, which by the same token, is not equal to $\displaystyle a^{\frac{1}{2}} + b^{\frac{1}{2}}$.