Question

Enumere a primeira coluna de acordo com segunda coluna de o valor da raiz de x: ( 1 ) 12x² = 0;
( 2 ) x² - 64 = 0
( 3 ) x² - 1 = 0
( 4 ) x² -2 x = 0
( 5 ) 12x² - 48 = 0
( ) ( +8, -8 )
( ) ( 0, 0 )
( ) ( 0 ,+ 2)
( ) ( +1, -1 )
( ) ( + 2, - 2 )

d ) 2 – 1 – 4 – 3 – 5; c ) 2 – 4 – 1 – 5 – 3; a) 5 – 2 – 1 – 4 – 3; b ) 4 – 2 – 1 – 3 – 5;

Answer 1

Resolvendo as equações primeiro:

( 1 )

$\begin{array}{l}\sf 12x^2=0\\\\\sf \dfrac{12x^2}{12}=\dfrac{0}{12}\\\\\sf x^2=0\\\\\sf \sqrt{x^2}=\sqrt{0}\\\\\sf |x|=0\\\\\sf \therefore~x'=x''~\Rightarrow~0\end{array}$

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( 2 )

$\begin{array}{l}\sf x^2-64=0\\\\\sf 64+x^2-64=0+64\\\\\sf x^2=64\\\\\sf \sqrt{x^2}=\sqrt{64}\\\\\sf |x|=8\\\\\sf x=\pm~8\\\\\sf \therefore~x'=8\quad e\quad x''=-8\end{array}$

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( 3 )

$\begin{array}{l}\sf x^2-1=0\\\\\sf 1+x^2-1=0+1\\\\\sf x^2=1\\\\\sf \sqrt{x^2}=\sqrt{1}\\\\\sf |x|=1\\\\\sf x=\pm~1\\\\\sf \therefore~x'=1\quad e\quad x''=-1\end{array}$

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( 4 )

$\begin{array}{l}\sf x^2-2x=0\\\\\sf x(x-2)=0\\\\\begin{cases}\sf x=0\\\\\sf x-2=0\end{cases}\\\\\begin{cases}\sf x'=0\\\\\sf x''=2\end{cases}\end{array}$

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( 5 )

$\begin{array}{l}\sf 12x^2-48=0\\\\\sf 48+12x^2-48=0+48\\\\\sf 12x^2=48\\\\\sf \dfrac{12x^2}{12}=\dfrac{48}{12}\\\\\sf x^2=4\\\\\sf \sqrt{x^2}=\sqrt{4}\\\\\sf |x|=2\\\\\sf x=\pm~2\\\\\sf \therefore~x'=2\quad e\quad x''=-2\end{array}$

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Assim relacionando a primeira coluna com a segunda:

( 2 ) => S = {8 ; -8}

( 1 ) => S = { 0 }

( 4 ) => S = {0 ; 2}

( 3 ) => S = {1 ; - 1}

( 5 ) => S = {2 ; -2}

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RESPOSTA: dessa forma a alternativa que se encaixa é: Letra D)

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Att. Nasgovaskov