Question

Решите систему уравнений

Answer 1

(x - y)² + (x - y) - 2 = 0

x² + y² = 41

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x - y = t

t² + t - 2 = 0

D = 1 + 8 = 9

t12=(-1 +- 3)/2 = 1  -2

(t + 2)(t - 1) = 0

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(x - y - 1)(x - y + 2) = 0

1. x - y - 1 = 0

x = y + 1

(y + 1)² + y² = 41

2y² + 2y - 40 = 0

y² + y - 20 = 0

D = 1 + 80 = 81

y12=(-1 +- 9)/2 = -5  4

y=-5    x = y + 1 = -4

y = 4  x = y + 1 = 5

2. x - y + 2 = 0

x = y - 2

(y - 2)² + y² = 41

y² - 4y + 4 + y² = 41

2y² -4y -37 = 0

D = 16 + 4*2*37 =  312

y12 = (4 +- 2√78)/4 = 1 +- √(39/2)

x12 = -1 +- √(39/2)

ответ (-4, -5) (5,4) ( -1 + √(39/2), 1 +√(39/2))  ( -1 - √(39/2), 1 -√(39/2))