Question

Как это решать заменой?

Answer 1

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Answer 2

((x - 3)/(x + 2))^2 - 15 = 16((x + 2)/(x - 3))^2

((x - 3)/(x + 2))^2  = t > 0

одз x ≠ -2  x ≠ 3

t - 15 = 16/t

t² - 15t - 16 = 0

D = 15^2 + 4*16 = 225 + 64 = 289 = 17^2

t12 = (15 +- 17)/2 = -1   16

t1 = -1 нет < 0

t2 = 16

((x - 3)/(x + 2))^2  = 16   |*(x + 2)^2

(x - 3)^2  = 16(x + 2)^2

(x - 3)^2  - (4(x + 2))^2 = 0

a² - b² = (a - b)(a + b)

(x - 3 - 4(x + 2))*(x - 3 + 4(x + 2)) = 0

(-3x - 11)(5x + 5) = 0

-3x - 11 = 0

x1 = -11/3

5x + 5 = 0

x2 = -1

Ответ x = {-1, -11/3}