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Question Number 66472 by hmamarques1994@gmail.com last updated on 15/Aug/19

$$\{\begin{array}{l}\sqrt[\sqrt{6}]{\mathbf{x}}+\sqrt[\sqrt{5}]{\mathbf{y}}=11\\ \frac{\sqrt[\sqrt{5}]{\mathbf{y}}}{\sqrt[\sqrt{6}]{\mathbf{x}}}=1\frac{1}{5}\end{array}$$$$$$$$\mathbf{Qual}\acute{\mathbf{e}}\mathbf{o}\mathbf{par}\mathbf{ordenado}\mathbf{na}\mathbf{forma}{\mathbf{a}}^{\sqrt{\mathbf{p}}}\mathbf{e}{\mathbf{b}}^{\sqrt{\mathbf{q}}}$$$$\mathbf{que}\mathbf{satisfaz}\mathbf{o}\mathbf{sistema}\mathbf{como}\mathbf{possivel}\mathbf{e}\mathbf{determinado}?$$

Answered by MJS last updated on 15/Aug/19

$$p=\sqrt[\sqrt{6}]{x}=x^{\frac{\sqrt{6}}{6}}$$$$\mathrm{similar}q=y^{\frac{\sqrt{5}}{5}}$$$$p+q=11$$$$\frac{q}{p}=\frac{6}{5}$$$$\Rightarrow$$$$p=5$$$$q=6$$$$\Rightarrow$$$$x=5^{\sqrt{6}}\approx 51.5371$$$$y=6^{\sqrt{5}}\approx 54.9540$$

Commented by hmamarques1994@gmail.com last updated on 15/Aug/19

$$\mathit{B}\mathit{o}\mathit{m}!$$

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