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Let $a,b$ and $c$ be real and positive parameters. Solve the equation

$$\sqrt{a+bx}+\sqrt{b+cx}+\sqrt{c+ax}=\sqrt{b-ax}+\sqrt{c-bx}+\sqrt{a-cx}$$

What could I do? Should take the square of both sides?

jimjim
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Danae Kissinger
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    Hint: $x=0$ is solution (trivial solution). LHS is increasing on $x$; RHS is decreasing on $x$. So, $x=0$ is unique solution. – Oleg567 Oct 06 '13 at 11:26

1 Answers1

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Oleg567's comment & hint as answer.

$x=0\,$ is a (trivial) solution. The LHS is increasing in $x$; the RHS is decreasing in $x$. So, $x=0$ is unique solution.

Hanno
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