<s>[INST] Equation with $ \sqrt[5]{}$ How to show that this equation $ \sqrt[5]{20-2x} + \sqrt[5]{7-x}+\sqrt[5]{3x+5}=2$ have 3 solutions 9, -6 and -25
Wolframsays  the equation have no solutions !
 [/INST] If $\sqrt[5]{20-2x}= a$  etc.,   $a+b+c=2$
$$a^5+b^5+c^5=32=(a+b+c)^5$$
Use How to factor $(a +b+c) ^5 -(a^5+ b^5 + c^5)$? to discover that $(a+b)(b+c)(c+a)=0$ should give three solutions.
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