√(x-1)+ √(x+3) +2√(x-1)(x+3) = 4-2x

Question

√(x-1)+ √(x+3) +2√(x-1)(x+3) = 4-2x

Answer 1

√(x-1) +√(x+3) +2√(x-1)(x+3) = 4-2x
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x>=1

(x-1) +2√(x-1)(x+3) +(x+3) +√(x-1) +√(x+3) -6 =0 <=>
(√(x-1) +√(x+3))^2 +√(x-1) +√(x+3) -6 =0 <=>
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t= √(x-1) +√(x+3)
t^2 +t -6 =0
t1=-3 (t>0)
t2=2

√(x-1) +√(x+3) =2 <=>
(√(x-1) +√(x+3))(√(x-1) -√(x+3)) =2(√(x-1) -√(x+3)) <=>
(x-1) -(x+3) =2(√(x-1) -√(x+3)) <=>
√(x-1) -√(x+3) =-2

√(x-1) +√(x+3) =2 
√(x-1) -√(x+3) =-2
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2√(x-1)=0 <=> x=1