Question

3x ao quadrado + 1/2 x = 2/3

Answer 1

Resposta:

Explicação passo-a-passo:

3x²+1/2x=2/3

mmc(2,3)=6

18x²+3x=4

18x²+3x-4=0

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~18x^{2}+3x-4=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=18{;}~b=3~e~c=-4\\\\\Delta=(b)^{2}-4(a)(c)=(3)^{2}-4(18)(-4)=9-(-288)=297\\\sqrt{\Delta} =\sqrt{297}=\sqrt{3^{2}.33}=3\sqrt{33}\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(3)-3\sqrt{33}}{2(18)}=-\frac{1+\sqrt{33}}{12}\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(3)+3\sqrt{33}}{2(18)}=\frac{-1+\sqrt{33}}{12}\\\\\\S=\{-\frac{1+\sqrt{33}}{12},~\frac{-1+\sqrt{33}}{12}\}$