Решите систему x+y=3x²-xy-y²=1

Question

Решите систему
x+y=3
x²-xy-y²=1

Answer 1

X + Y = 3 
Y = 3 - X 
Y^2 = 9 - 6X + X^2 
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X^2 - XY - Y^2 = 1 
X^2 - X*( 3 - X) - 9 + 6X - X^2 = 1 
X^2 - 3X + X^2 - 9 + 6X - X^2 - 1 = 0 
X^2 + 3X - 10 = 0 
D = 9 + 40 = 49 ; √ D = 7 
X1 = ( - 3 + 7) : 2 = 2 
X2 = ( - 3 - 7 ) : 2 = - 5 
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Y = 3 - X 
Y1 = 3 - 2 = 1 
Y2 = 3 + 5 = 8