Question

rezolvați sistemul
${x}^{3} - {y}^{3} = 7 \\ {x}^{2} + xy + {y}^{2} = 7$
vă roooog nu-mi iese​

Answer 1

x³-y³ = 7

x²+xy+y² = 7

x³-y³ = 7

=> (x-y)(x²+xy+y²) = 7

=> (x-y)•7 = 7 => x-y = 1

(x-y)² = x²-2xy+y²

1 = x²+xy+y²-3xy

1 = 7-3xy

=> -3xy = -6 => xy = 2

x-y = 1 => x = y+1

xy = 2 => (y+1)y = 2 => y²+y-2 = 0

Delta = 1+8 = 9 => y1 = (-1-3)/2 = -2

=> y2 = (-1+3)/2 = 1

(1) y = -2 => x•(-2) = 2 => x = -1

(2) y = 1 => x•1 = 2 => x = 2

=> (x,y) = { (-1;-2), (2,1) }