[tex] \left \{ {{xy+x+y=11} \atop {x^{2}y+y x^{2}=30}} \right. [/tex]
se introduc necunoscutele auxiliare
s=x+y si p=xy
atunci sistemul devine:
[tex] \left \{ {{p+s=11} \atop {p\cdot s}=30}} \right. \\ \\ \( 11-s)\cdot s=30 \\ \\ s^{2} -11s+30=0 \\ \\ [/tex]
Δ=b²-4ac=121-120=1
x₁=(-b+√Δ)/2a=(11+1)/2=6
x₂=(-b-√Δ)/2a=(11-1)/2=5
p₁+s₁=11⇒p₁=11-6=5
p₂+s₂=11⇒p₂=11-5=6
