✅ Após desenvolver os cálculos, concluímos que o resultado esperado da referida expressão algébrica é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf 225\:\:\:}}\end{gathered}$}[/tex]
Portanto, a opção correta é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf Alternativa\:E\:\:\:}}\end{gathered}$}[/tex]
Seja a equação:
[tex]\Large\displaystyle\text{$\begin{gathered} 2x^{2} + 2y^{2} = 30\end{gathered}$}[/tex]
Dividindo ambos os membros por "2", temos:
[tex]\Large\displaystyle\text{$\begin{gathered} \frac{2x^{2}}{2} + \frac{2y^{2}}{2} = \frac{30}{2}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \bf I\end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered} x^{2} + y^{2} = 15\end{gathered}$}[/tex]
Se estamos querendo encontrar:
[tex]\Large\displaystyle\text{$\begin{gathered} \bf II\end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered} (x^{2} + y^{2})^{2} = \:?\end{gathered}$}[/tex]
Então, basta substituir "I" em "II":
[tex]\Large\displaystyle\text{$\begin{gathered} (x^{2} + y^{2})^{2} = 15^{2} = 15\cdot 15=225\end{gathered}$}[/tex]
✅ Portanto, o resultado procurado é:
[tex]\Large\displaystyle\text{$\begin{gathered} 225\end{gathered}$}[/tex]
[tex]\LARGE\displaystyle\text{$\begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered}$}[/tex]
Saiba mais:
Letra E.
[tex]2x {}^{2} + 2y {}^{2} = 30 \: \: \: \: \: \: \: \: \: : (2) \\x {}^{2} + y {}^{2} = 15 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ [/tex]
[tex](x {}^{2} + y {}^{2} ) {}^{2} \\ 15 {}^{2} \\ \boxed{\boxed{\boxed{225}}} \\ [/tex]
att. yrz
