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a) |x+1|=3|x-1|
x+1 ; x≥-1
|x+1|={ -x-1 ; x<-1
x-1 ; x≥1
|x-1|={ -x+1 ; x<1
1. (-∞,-1)
-x-1=3(-x+1)
-x-1=-3x+3
2x=2
x=1
2. <-1,1)
x+1=3(-x+1)
x+1=-3x+3
4x=2
x=1/2
3. <1,+∞)
x+1=3(x-1)
x+1=3x-3
-2x=-4
x=2
b) |√3+2x|=|1-√3x|
√3+2x ; x≥-√3/2
|√3+2x|={ -√3-2x ; x<-√3/2
1-√3x ; x≤1/√3 x≤√3/3
|1-√3x|={ -1+√3x ; x>1/√3 x>√3/3
1. (-∞,-√3/2)
-√3-2x=1-√3x
-2x+√3x=1+√3
x(-2+√3)=1+√3
x=(1+√3)/(-2+√3)=(-1-√3)/3-4=1+√3
2. <-√3/2,√3/3>
√3+2x=1-√3x
2x+√3x=1-√3
x(2+√3)=1-√3
x=(1-√3)/(2+√3)=(3√3-5)/3-4=5-3√3
3. (√3/3,+∞)
√3+2x=-1+√3x
2x-√3x=-1-√3
x(2-√3)=-1-√3
x=(-1-√3)/(2-√3)=(-3√3-5)/4-3=-3√3-5
d) √(2x²-2√6x+3)=√(3x²+2√6x+2)
2x²-2√6x+3=3x²+2√6x+2
-x²-4√6x=-1
x(-x-4√6)=-1
x=-1 v -x-4√6=-1
-x=-1+4√6
x=1-4√6