Question

Решите систему уравнения x^2+z^2=5 x^4-z^4=15​

Answer 1

a² - b² = (a - b)(a + b)

x^2 + z^2 = 5

x^4 - z^4 = 15

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x^4 - z^4 = (x^2 - z^2)(x^2 + z^2) = 5(x^2 - z^2) = 15

x^2 - z^2 = 3

Складываем

x^2 - z^2 + x^2 + z^2 = 5 + 3

2x^2 = 8

x^2 = 4

1. x = 2

4 + z^2 = 5

z^2 = 1

z12 = +- 1

2. x = -2

(-2)^2 + z^2 = 5

z^2 = 1

z12= +- 1

ответ (2,1) (2,-1)(-2,1)(-2,-1)