X^2+y^2=5 x^4-y^4=15 решите систему уравнений

Question

X^2+y^2=5 x^4-y^4=15 решите систему уравнений

Answer 1

Х^2 = а ; х^4 = а^2
y^2 = b ; y^4 = b^2
a + b = 5
a^2 - b^2 = 15
a = 5 - b
a^2 = 25 - 10b + b^2
25 - 10b + b^2 - b^2 = 15
25 - 10b = 15
10b = 10
b = 1
a = 5 - 1 = 4
X^2 = a
X^2 = 4
X1 = 2 ; X2 = - 2
y^2 = b
y^2 = 1
y1 = 1 ; y2 = - 1
Ответ ( 2 ; 1 ) ; ( - 2 ; - 1 )