Question

Resolva aa operações fracionarias 5/x2+1/x=6

Answer 1

Resposta:

S={-5/6, 1}

Explicação passo-a-passo:

$\frac{5}{x^{2}}+\frac{1}{x}=6$

mmc(x²,x,1)

x²,x|x

x,1|x

1,1/ =x.x=x²

$\displaystyle\frac{5}{x^{2}}+\frac{1}{x}=6\\\\\frac{5+x}{x^{2}}=\frac{6x^{2}}{x^{2}}\\\\5+x=6x^{2}\\6x^{2}-x-5=0\\Aplicando~a~f\'{o}rmula~de~Bhaskara~para~6x^{2}-1x-5=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=6{;}~b=-1~e~c=-5\\\Delta=(b)^{2}-4(a)(c)=(-1)^{2}-4(6)(-5)=1-(-120)=121\\\sqrt{\Delta}=\sqrt{121}=11\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-1)-11}{2(6)}=-\frac{10\div2}{12\div2}=-\frac{5}{6}\\x^{"}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-1)+11}{2(6)}=\frac{12}{12}=1$