Verified answer

|x| = x, x >= 0

    = -x, x < 0

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5x + |x| = -9

x >= 0

5x + x = -9

6x = -9

x = -3/2 нет

x < 0

5x - x = -9

4x = -9

x = -9/4

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|x^2-4x+2|=1

1. x^2-4x+2=1

x^2-4x+1=0

D = 16 - 4 = 12

x₁₂ = (4 +- √12)/2 = 2 ± √3

2. x^2-4x+2=-1

x^2-4x+3=0

D = 16 - 12 = 4

x₃₄ = (4 +- 2)/2 = 1   3

x = {1,3, 2 ± √3}

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x^2-|5x|+6=0

|x|^2 = x^2

|x| = y >=0

y^2 - 5y + 6 = 0

D = 25 - 24 = 1

y₁₂ = (5 +- 1)/2 = 2    3

1. y = 2

|x| = 2

x₁₂ = ± 2

2. y = 3

|x| = 3

x₃₄ = ± 3