Question

√x-1+√x+3 +2√(х-1)(x+3) (это под одним корнем) =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

Пошаговое объяснение: