Question

Решите систему х^2+у^2=74 х-у=2

Answer 1

x²+(x-2)²=74
x²+x²-4x+4-74=0
2x²-4x-70=0
x²-2x-35=0
D=1+35=36
x₁=1+√D=1+6=7
x₂=1-√D=1-6=-5

y₁=x₁-2=7-2=5
y₂=x₂-2=-5-2=-7

Проверка
1) x=7; y=5
x-y = 7-5 = 2
x²+y² = 7²+5² = 49+25 = 74 - верно

2) x=-5; y=-7
x-y = -5-(-7) = 2
x²+y² = (-5)²+(-7)² = 25+49 = 74 - верно

Ответ: (x=7; y=5) или (x=-5; y=-7)