Х+у=1 х=1-у х=1-у х=1-у x=1-y
х²+у²=9 (1-у)² +у² = 9 1-2у+у²+у²-9=0 2у²-2у-8 = 0 y²-y-4=0
D = (-1)²-4*1*(-4) = 1+16=17
y₁=(1-√17)/2 x₁= 1-(1-√17)/2=(2-1+√17)/2 = (1+√17)/2
y₂=(1+√17)/2 x₂ = 1-(1+√17)/2=(2-1-√17)/2 = (1-√17)/2
Проверка:
(1-2√17+17)4+(1+2√17+17)/4 = 9
(1-2√17+17+1+2√17+17)/4=9
36/4=9
9=9