Prove that $a^{\frac {1}{4}}+b^{\frac {1}{4}}+c^{\frac {1}{4}}=0\Rightarrow a+b+c =2(\sqrt {ab}+\sqrt {bc}+\sqrt {ca})$ If $a^{\frac {1}{4}}+b^{\frac {1}{4}}+c^{\frac {1}{4}}=0$, prove that $a+b+c =2(\sqrt {ab}+\sqrt {bc}+\sqrt {ca})$.
I guess that the given expression is true if and only if $a=b=c=0$. Is it true? Or,is there any other alternatives? 

Maybe you mean that 
$$2(\sqrt{ab}+\sqrt{ac}+\sqrt{bc})-a-b-c=$$
$$=(\sqrt[4]a+\sqrt[4]b+\sqrt[4]c)(\sqrt[4]a+\sqrt[4]b-\sqrt[4]c)(\sqrt[4]a-\sqrt[4]b+\sqrt[4]c)(-\sqrt[4]a+\sqrt[4]b+\sqrt[4]c),$$
which is not necessary. 
