Question

sendo A=x ao quadrado + 1 e B =-2x ao quadrado + x+ 2, determine no caderno o valor de:

a) A+B b)A-B c) B-A
​

Answer 1

✅ Após resolver os cálculos, concluímos que os resultados da referidas expressões algébricas são, respectivamente:

   $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf a)\:\:\:A + B = -x^{2} + x + 3\:\:\:}}\end{gathered} }$

    $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf b)\:\:\:A - B = 3x^{2} - x - 1\:\:\:}}\end{gathered} }$

   $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf c)\:\:\:B - A = -3x^{2} + x + 1\:\:\:}}\end{gathered} }$

Sejam as expressões algébricas:

          $\Large\begin{cases} A = x^{2} + 1\\B = -2x^{2} + x + 2\end{cases}$

• a)    Calculando A + B:

          $\Large\displaystyle\begin{gathered} A + B = (x^{2} + 1) + (-2x^{2} + x + 2)\end{gathered}$

                          $\Large\displaystyle\begin{gathered} = x^{2} + 1 - 2x^{2} + x + 2\end{gathered}$

                          $\Large\displaystyle\begin{gathered} = -x^{2} + x + 3\end{gathered}$

        Portanto:

           $\Large\displaystyle\begin{gathered} A + B = -x^{2} + x + 3\end{gathered}$

• b)   Calculando A - B:

           $\Large\displaystyle\begin{gathered} A - B = (x^{2} + 1) - (-2x^{2} + x + 2)\end{gathered}$

                           $\Large\displaystyle\begin{gathered} = x^{2} + 1 +2x^{2} - x - 2\end{gathered}$

                           $\Large\displaystyle\begin{gathered} = 3x^{2} - x - 1\end{gathered}$

        Portanto:

            $\Large\displaystyle\begin{gathered} A - B = 3x^{2} - x - 1\end{gathered}$

• c)   Calculando B - A:

            $\Large\displaystyle\begin{gathered} B - A = (-2x^{2} + x + 2) - (x^{2} + 1)\end{gathered}$

                            $\Large\displaystyle\begin{gathered} = -2x^{2} + x + 2 - x^{2} - 1\end{gathered}$

                            $\Large\displaystyle\begin{gathered} = -3x^{2} + x + 1\end{gathered}$

         Portanto:

             $\Large\displaystyle\begin{gathered} B - A = -3x^{2} + x + 1\end{gathered}$

$\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered} }$

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