How to Find X in a Quadratic Equation?

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Homework Statement


\frac{2-x}{2+x}=t^3
How to find x?




Answer is
x=\frac{2-2t^3}{1+t^3}
 
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Start by multiplying both sides of the equation by (x+2).
 
ytpj said:
\frac{2-x}{2+x}=t^3
How to find x?

Reminds me of this very old one :biggrin:

(but seriously, do what quasar987 told you)
 
I don't understand where this leading. It still will be
2-x=2t^3+xt^3 so what?
 
Then send everything on the same side of the equation so that you get

2-x-2t^3+xt^3=0

and factor the x.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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