Question

Решите уравнение:
$\sqrt{ \frac{x}{x - 1} } - 0.5 = 3 \sqrt{1 - \frac{1}{x} }$
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Answer 1

√x/(x - 1) - 0.5 = 3√(1 - 1/x)

√x/(x - 1) - 0.5 = 3√(x - 1)/x
одз
(x - 1)/x >= 0
x/(x - 1) >= 0
+++++++++(0) --------------- (1) ++++++++
x ∈ (-∞ 0) U (1 +∞)
√x/(x - 1) = y > 0
y - 1/2 = 3/y
2y - 1 = 6/y
2y² - y - 6 = 0
D = 1 + 48 = 49
y12 = (1 +- 7)/4 = 2    -3/2
-3/2 < 0 нет
y = 2
√x/(x - 1) = 2
x/(x - 1) = 4
x = 4x - 4
3x = 4
x = 4/3