Question

$\sqrt{x - 1} = 3 - x$
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Answer 1

Resposta:

x=2

Explicação passo-a-passo:

$\sqrt{x - 1} = 3 - x\\(\sqrt{x-1} )^{2}=(3-x)^{2}\\x-1=9-6x+x^{2}\\x^{2}-7x+10=0\\\\Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-7x+10=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-7~e~c=10\\\\\Delta=(b)^{2}-4(a)(c)=(-7)^{2}-4(1)(10)=49-(40)=9\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-7)-\sqrt{9}}{2(1)}=\frac{7-3}{2}=\frac{4}{2}=2\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-7)+\sqrt{9}}{2(1)}=\frac{7+3}{2}=\frac{10}{2}=5$

$\sqrt{x-1}=3-x\\\\Para~x=2\\\sqrt{2-1}=3-2\\\sqrt{1} =1\\1=1~(Verdadeiro)\\\\Para~x=5\\\sqrt{5-1}=3-5\\\sqrt{4} =-2\\2=-2~(Falso)$