# An algebra problem by ismet cosic

Algebra Level pending

$\large \begin{cases} x^{z}=y^{\frac{8}{3}} \\ y^{z}=x^{\frac{2}{3}} \\ z=\sqrt[4]{x}+\sqrt[4]{y} \end{cases}$

There are two triplets $$(x,y,z)$$ of solutions to this system of equations, one of which is $$(1,1,2)$$. If the other set is $$(a,b,c)$$, what is the value of $$\dfrac{\sqrt{a}}{b} \times c$$ rounded to three decimal places?

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