Question

resolva a equação irracional:
√2x+1 +1=x

me ajudem, pfv

Answer 1

Resposta:

√(2x)+1 +1=x

√(2x)+2=x

√(2x)=x-2

[√(2x)]²=(x-2)²

2x=x²-4x+4

x²-4x-2x+4=0

x²-6x+4=0

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-6x+4=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-6~e~c=4\\\\\Delta=(b)^{2}-4(a)(c)=(-6)^{2}-4(1)(4)=36-(16)=20\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-6)-\sqrt{20}}{2(1)}=\frac{6-2\sqrt{5}}{2}=3-\sqrt{5}\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-6)+\sqrt{20}}{2(1)}=\frac{6+2\sqrt{5}}{2}=3+\sqrt{5}\\\\S=\{3-\sqrt{5},~3+\sqrt{5}\}$