Question

6) Resolva a equação: x² - x - 1 = 1 *

5 pontos

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Answer 1

Resposta:

Explicação passo-a-passo:

x²-x-1=1

x²-x-1-1=0

x²-x-2=0

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-x-2=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-1~e~c=-2\\\\\Delta=(b)^{2}-4(a)(c)=(-1)^{2}-4(1)(-2)=1-(-8)=9\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-1)-\sqrt{9}}{2(1)}=\frac{1-3}{2}=\frac{-2}{2}=-1\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-1)+\sqrt{9}}{2(1)}=\frac{1+3}{2}=\frac{4}{2}=2\\\\S=\{-1,~2\}$