Question

Determine o conjunto solução

Answer 1

$\begin{cases}x+y^2=50~~(i)\\ \log_y(x)=2~~(ii)\end{cases}\\\\\\ y^2=50-x\Rightarrow y= \sqrt{50-x} \\\\\\ \log_y(x)=2\\ \log_{ \sqrt{50-x}}(x)=2\\\\ ( \sqrt{50-x} )^2=x\\ 50-x=x\\ 2x=50\\\\ \boxed{x=25}\\\\\\ x+y^2=50\\ 25+y^2=50\\ y^2=25\\ y= \sqrt{25}\\\\ \boxed{y=5}\\\\\\ \Large\boxed{\text{S}=\{25,5\}}$