Question

Resolva as seguintes equações sendo U=R :
a) 4x-x²=0 continuação -x²+4x=0
b)9x²-1=0
c) (3x-1)²+(x-2)² 
d) (-x²+1),(x²-3x+2)=0


para hoje porfavor

Answer 1

E aí mano,

$4x- x^{2} =0\\ - x^{2} +4x=0~~*~~(-1)\\ x^2-4x=0\\ x(x-4)=0\\\\ \begin{cases}x'=0~~e~~x-4=0\\ ~~~~~~~~~~~~~x''=4\end{cases}\\\\\\ \boxed{S=\{0,4\}}$

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$9 x^{2} -1=0\\ 9x^2=1\\\\ x^{2} = \dfrac{1}{9}\\\\ x=\pm \sqrt{ \dfrac{1}{9} }\\\\ x=\pm \dfrac{1}{3}\\\\\\ \boxed{S=\left\{ \dfrac{1}{3},- \dfrac{1}{3}\right\}}$

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$(3x-1)^2+(x-2)^2=0\\ 9x^2-6x+1+x^2-4x+4=0\\ 10x^2-10x+5=0~~\div~~5\\ 2x^2-2x+1=0\\\\ \Delta=b^2-4ac\\ \Delta=(-2)^2-4*2*1\\ \Delta=4-8\\ \Delta=-4~~\Delta<0~~\therefore~~\mathbb{U}\not\subset \mathbb{R}$

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$(-x^2+1)( x^{2} -3x+2)=0\\\\ (-x^2+1)=0*(-1)\\ x^2-1=0\\ x^2=1\\ x=\pm \sqrt{1}\\ x=\pm1\\\\ x'=1\\ x''=-1$

$x^{2} -3x+2=0\\\\ \Delta=b^2-4ac\\ \Delta=(-3)^2-4*1*2\\ \Delta=9-8\\ \Delta=1\\\\ x= \dfrac{-b\pm \sqrt{\Delta} }{2a}= \dfrac{-(-3)\pm \sqrt{1} }{2*1}= \dfrac{3\pm1}{2}\begin{cases}x'= \dfrac{3-1}{2}= \dfrac{2}{2}=1\\\\ x''= \dfrac{3+1}{2}= \dfrac{4}{2}=2 \end{cases}\\\\\\ \boxed{S=\{1,-1,~1,2\}}$

Tenha ótimos estudos =))