Question

$resolva \: a \: equaca o \: de \:segundo \: grau \\ {x}^{2} - x - 1 = 0$
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Answer 1

Resposta:

Explicação passo-a-passo:

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