Question

Se $\mathsf{x^2 - x - 1 = 0}$, então qual é o valor de $\mathsf{x^3 - 2x + 1}$?

Answer 1

$\large\begin{array}{l} \textsf{Se}\\\\ \mathsf{x^2-x-1=0,}\qquad\textsf{com }\mathsf{x\in \mathbb{R},\qquad(i)}\\\\\\ \textsf{ent\~ao}\\\\ \mathsf{x\cdot (x^2-x-1)=x\cdot 0}\\\\ \mathsf{x^3-x^2-x=0}\qquad\mathsf{(ii)} \end{array}$



$\large\begin{array}{l} \textsf{Somando }\mathsf{(ii)~e~(i)}\textsf{ membro a membro, obtemos}\\\\ \mathsf{(x^3-x^2-x)+(x^2-x-1)=0+0}\\\\ \mathsf{x^3-\diagup\!\!\!\! x^2+\diagup\!\!\!\! x^2-x-x=1}\\\\ \mathsf{x^3-2x=1}\\\\ \mathsf{x^3-2x+1=1+1}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{x^3-2x+1=2} \end{array}}\qquad\checkmark \end{array}$


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$\large\begin{array}{l} \textsf{D\'uvidas? Comente.}\\\\\\ \textsf{Bons estudos! :-)} \end{array}$


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