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
z12= +- 1
ответ (2,1) (2,-1)(-2,1)(-2,-1)
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Verified answer
a² - b² = (a - b)(a + b)
x^2 + z^2 = 5
x^4 - z^4 = 15
---
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)
написано Решите систему уравнения x^2+z^2=5 x^4-z^4=15
они аналогично решаются
a² - b² = (a - b)(a + b)
3. (x^2 - z^2)(x^2 + z^2) = 15
4/ x(x^2+z^2) = 10
z(x^2 + z^2) = 5