Solving Quadratic Equations: How to Solve P + N = C + 2/C for C

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Homework Statement



P + N =C + 2/C

solve for C

Homework Equations



I have tried all algebraic methods I can think of and can't solve for C.

The Attempt at a Solution



I ended up with C(N + P) = C^2 + 2
 
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zeromodz said:

Homework Statement



P + N =C + 2/C

solve for C

Homework Equations



I have tried all algebraic methods I can think of and can't solve for C.

The Attempt at a Solution



I ended up with C(N + P) = C^2 + 2

Write it as C^2-C(N+P)-2=0. It's a quadratic equation in C, right? How do you solve quadratics?
 
Dick said:
Write it as C^2-C(N+P)-2=0. It's a quadratic equation in C, right? How do you solve quadratics?

Oh okay, I use the quadratic formula. I understand now thanks!
 
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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