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**The asks for us to find the nature of roots of the following equation ,i.e,rational or irrational nature of the roots:**

the Equation is :http://www5a.wolframalpha.com/Calculate/MSP/MSP7106108efdacf0gb84ie000039f29d33b6hie7ic?MSPStoreType=image/gif&s=56&w=63.&h=18.x^5+x=5

the Equation is :

I have been able to prove that this equation has one positive real root through the use of calculus (it is an increasing function) and the fact that it is an positive real root through Descartes' rule of signs.I would love to get some help in trying to solving the problem.