Question

obtenha, em R(reais), o conjunto solução da equação do 2° grau completa. -x²+7x-2=0

Answer 1

$-x^2+7x-2=0\\\\\text{coeficiente:}\\\\a=-1\qquad\qquad{b}=7\qquad\qquad{c}=-2\\\\\mathrm{F\acute{o}rmula\ de\ Bh\acute{a}skara:}\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\quad\text{em que }\Delta=b^2-4\cdot{a}\cdot{c}\\\\\\\text{Substituindo os valores dos coeficientes, temos:}\\\\x=\dfrac{-b\pm\sqrt{b^2-4\cdot{a}\cdot{c}}}{2a}\\\\\\x=\dfrac{-(7)\pm\sqrt{(7)^2-4\cdot{(-1)}\cdot{(-2)}}}{2(-1)}\\\\\\x=\dfrac{-7\pm\sqrt{49-8}}{-2}\\\\\\x=\dfrac{-7\pm\sqrt{41}}{-2}\left\langle\begin{matrix}x'=\dfrac{-7+\sqrt{41}}{-2}\longrightarrow{x}=-\dfrac{-7+\sqrt{41}}{2}\longrightarrow{x}=\dfrac{7-\sqrt{41}}{2}\\\\\\x''=\dfrac{-7-\sqrt{41}}{-2}\longrightarrow{x}=-\dfrac{-7-\sqrt{41}}{2}\longrightarrow{x}=\dfrac{7+\sqrt{41}}{2}\end{matrix}\right\\\\\\\\\boxed{S=\left\{\dfrac{7-\sqrt{41}}{2},\ \dfrac{7+\sqrt{41}}{2}\right\}}$

Answer 2

$ Ola Rose

-x²+7x-2=0delta
d² = 49 - 8 = 41
d = √41

x1 = (-7 + √41)/-2 = (7 - √41)/2
x2 = (-7 - √41)/-2 = (7 + √41)/2

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