Verified answer

x/y - y/x = 15/4

x² + y² = 1377

решим первое x/y = t     y/x = 1/t

t - 1/t = 15/4

4(t² - 1) = 15 t

4t² - 15t - 4 = 0

D = 15² - 4*(-4)*4 = 225 + 64 = 289

t12 = (15 +- 17)/8 = 4    -1/4

1. t1=4

x/y = 4

x = 4y

одного знака x y

16y² + y² = 1377

17y² = 1377

y² = 81

|x|=9

y = 9

x = 4y = 36

y = -9

x = 4*(-9) = -36

2. t2 = -1/4

x/y = -1/4

y = -4x

разного знака

(-4x)² + x² = 1377

17x² = 1377

x² = 81

|x| = 9

x = 9

y = -4*9 = -36

x = -9

y = -4*(-9) = 36

ответ (-9, 36) (-36, - 9) (36, 9) (9, -36)