# How to solve (x-1)^2 * (a+x)=1

1. Jan 21, 2009

### steem84

I am a little bit confused about solving the following equation:

(x-1)2(a+x)=1

How to do this??

2. Jan 21, 2009

### NoMoreExams

Are you sure there's a simple way to solve that, given that you don't know a? It's a cubic...

3. Jan 21, 2009

### steem84

well, actually this is the original equation (see figure1)

The solution is in figure 2..

So let me reformulate my question: Can this be proven analytically?

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• ###### equation2.bmp
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4. Jan 21, 2009

### gabbagabbahey

This is very different from the problem in your first post!

Anyways, start by squaring both sides of the equation in the first link. Then multiply both sides by $$4((\rho^{*})^2+(x^{*})^2)$$ and simplify to obtain:

$$(\rho^{*})^6+((x^{*})^2-4a^2)(\rho^{*})^4+4a^2(a^2-(x^{*})^2)(\rho^{*})^2=0$$

That should tell you that either $$(\rho^{*})^2=0$$ or

$$(\rho^{*})^4+((x^{*})^2-4a^2)(\rho^{*})^2+4a^2(a^2-(x^{*})^2)=0$$

You can use the quadratic equation to solve the above expression for $$(\rho^{*})^2$$ and then take the square root to obtain the final solution.

5. Jan 22, 2009

### steem84

Yes, ok thank you. It did not cross my mind to substitute a variable for a variable^2