3√(3x² + 2x - 4) - 2x = 3x² - 2
3√(3x² + 2x - 4) = 3x² + 2x - 2
ограничения 3x² + 2x - 4 >= 0
D = 4 + 4*4*3 = 4 + 48 = 52
x12 = (-2 +- √52)/6 = (-1 +- √13)/3
+++++++(-1 +- √13)/3 ------------- (-1 + √13)/3 +++++++++
x ∈ (-∞, (-1 +- √13)/3] U [(-1 +- √13)/3, + ∞) ≈ (-∞, -4.6/3] U [2.6/3, +∞)
3√(3x² + 2x - 4) = (3x² + 2x - 4) + 2
√(3x² + 2x - 4) = t (>=0)
3t = t² + 2
t² - 3t + 1 = 0
t1 = 1
t2 = 2
1. t1 = 1
√(3x² + 2x - 4) = 1
3x² + 2x - 4 = 1
3x² + 2x - 5 = 0
D = 4 + 4*5*3 = 64
x12 = (-2 +- 8)/6 = 1 - 5/3
2. t2 = 2
√(3x² + 2x - 4) = 2
3x² + 2x - 4 = 4
3x² + 2x - 8 = 0
D = 4 + 4*8*3 = 100
x12 = (-2 +- 10)/6 = 4/3 - 2
ответ x = {-2, -5/3, 1, 4/3}
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Verified answer
3√(3x² + 2x - 4) - 2x = 3x² - 2
3√(3x² + 2x - 4) = 3x² + 2x - 2
ограничения 3x² + 2x - 4 >= 0
D = 4 + 4*4*3 = 4 + 48 = 52
x12 = (-2 +- √52)/6 = (-1 +- √13)/3
+++++++(-1 +- √13)/3 ------------- (-1 + √13)/3 +++++++++
x ∈ (-∞, (-1 +- √13)/3] U [(-1 +- √13)/3, + ∞) ≈ (-∞, -4.6/3] U [2.6/3, +∞)
3√(3x² + 2x - 4) = (3x² + 2x - 4) + 2
√(3x² + 2x - 4) = t (>=0)
3t = t² + 2
t² - 3t + 1 = 0
t1 = 1
t2 = 2
1. t1 = 1
√(3x² + 2x - 4) = 1
3x² + 2x - 4 = 1
3x² + 2x - 5 = 0
D = 4 + 4*5*3 = 64
x12 = (-2 +- 8)/6 = 1 - 5/3
2. t2 = 2
√(3x² + 2x - 4) = 2
3x² + 2x - 4 = 4
3x² + 2x - 8 = 0
D = 4 + 4*8*3 = 100
x12 = (-2 +- 10)/6 = 4/3 - 2
ответ x = {-2, -5/3, 1, 4/3}