x-1-6-y-1-5-11-y-1-5-x-1-6-1-1-5-Qual-e-o-par-ordenado-na-forma-a-p-e-b-q-que-satisfaz-o-sistema-como-possivel-e-determi

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

{\begin{cases} \sqrt[\sqrt{6}]{x} + \sqrt[\sqrt{5}]{y} = 11 \\ \frac{\sqrt[\sqrt{5}]{y}}{\sqrt[\sqrt{6}]{x}} = 1 \frac{1}{5} \end{cases}

Qual \overset{´}{e} o par ordenado na forma a^{\sqrt{p}} e b^{\sqrt{q}}

que satisfaz o sistema como possivel e determinado ?

Answered by MJS last updated on 15/Aug/19

p = \sqrt[\sqrt{6}]{x} = x^{\frac{\sqrt{6}}{6}}

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

B o m!