Question

16. Determine o valor de x.​

Answer 1

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$\tt a)~\sf 4\cdot x=9\cdot5\\\sf 4x=45\\\sf x=\dfrac{45}{4}\checkmark$

$\tt b)~\sf \diagup\!\!\!\!2x\cdot x=\diagup\!\!\!\!2\cdot9\\\sf x^2=9\\\sf x=\sqrt{9}\\\sf x=3\checkmark$

$\tt c)~\sf 9x=8\cdot11\\\sf x=\dfrac{88}{9}\checkmark$

$\tt d)~\sf x\cdot x=1\cdot(x+12)\\\sf x^2=x+12\\\sf x^2-x-12=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-1)^2-4\cdot1\cdot(-12)\\\sf\Delta=1+48\\\sf\Delta=49\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf x=\dfrac{-(-1)\pm\sqrt{49}}{2\cdot1}\\\sf x=\dfrac{1\pm7}{2}\begin{cases}\sf x_1=\dfrac{1+7}{2}=\dfrac{8}{2}=4\checkmark\\\sf x_2=\dfrac{1-7}{2}=-\dfrac{6}{2}=\diagup\!\!\!\!\!\!-\!\backslash\!\!\!\!\!\!\!3\end{cases}$