Question

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$(2x - 1) {}^{2} = (x + 2) {}^{2}$
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Answer 1

Resposta:

(2x-1)²=(x+2)²

4x²-4x+1=x²+4x+4

3x²-8x-3=0

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~3x^{2}-8x-3=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=3{;}~b=-8~e~c=-3\\\\\Delta=(b)^{2}-4(a)(c)=(-8)^{2}-4(3)(-3)=64-(-36)=100\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-8)-\sqrt{100}}{2(3)}=\frac{8-10}{6}=\frac{-2\div2}{6\div2}=-\frac{1}{3}\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-8)+\sqrt{100}}{2(3)}=\frac{8+10}{6}=\frac{18}{6}=3\\\\S=\{-\frac{1}{3},~3\}$