Question

como resolver essa equação
$b = x {}^{2} + x - 7 = 5$
?
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Answer 1

Resposta:

Explicação passo-a-passo:

x²+x-7=5

x²+x-7-5=0

x²+x-12=0

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}+x-12=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=1{;}~b=1~e~c=-12\\\\C\'alculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(1)^{2}-4(1)(-12)=1-(-48)=49\\\\C\'alculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(1)-\sqrt{49}}{2(1)}=\frac{-1-7}{2}=\frac{-8}{2}=-4\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(1)+\sqrt{49}}{2(1)}=\frac{-1+7}{2}=\frac{6}{2}=3\\\\S=\{-4,~3\}$