Question

решить систему x^3-y^3=26 x^2+xy+y^2=13

Answer 1

x³-y³=26

x²+xy+y²=13

x³-y³ = (x-y)(x²+xy+y²)=(x-y)*13 = 26

x-y = 26/13 = 2

x = y+2

(y+2)²+(y+2)y+y²=13

y²+4y+4+y²+2y+y² = 13

3y²+6y-9 = 0

y²+2y-3 = 0

(y-1)(y+3) = 0

y₁ = 1, x₁= 3

y₂ = -3, x₂=-1