Question

Cum se rezolva sistemul?
x+y=1
xy=-6

Answer 1

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

Introducem in a doua ecuatie

xy=(1-y)y=y-y^2

y-y^2=-6 /+6
y-y^2+6=0 /*(-1)
y^2-y-6=0

Δ=b^2-4ac=1-4*1*(-6)=1+24=25
y₁=(-b+√Δ)/2a=(1+5)/2=3 .............. x₁=1-y₁=1-3=-2
y₂=(1-5)/2=-2 ................. x₂=1-y₂=1-(-2)=1+2=3