Rozwiąż układy równań: a) [latex] left { {{x+y=5} atop {xy=6}} ight. [/latex] b) [latex] left { {{ x^{2} + y^{2}=25 } atop {xy=28}} ight. [/latex] c) [latex] left { {{ x^{2} - y^{2}=8 } atop {xy=3}} ight. [/latex] NA TERAZ... DAJĘ NAJ!

  [latex] left { {{x=5-y} atop {(5-y)y=6}} ight. [/latex] [latex] left { {{x=5-y} atop {5y-y^2=6}} ight. [/latex] -y^2+5y-6=0 Δ=25-24=1 y1 = [latex] frac{-5+1}{-2} [/latex] = 2 y2 = [latex] frac{-5-1}{-2} [/latex] = 3 x1 = 5-2 = 3 x2 = 5-3 = 2 [latex] left { {{x1=3} atop {y1=2}} ight. [/latex] [latex] left { {{x2=2} atop {y1=3}} ight. [/latex] [latex] left { {{x^2=25-y^2} atop {xy=28}} ight. [/latex] [latex] left { {{x=5-y} atop {(5-y)y=28}} ight. [/latex] [latex] left { {{x=5-y} atop {5y-y^2=28}} ight. [/latex] -y^2+5y-28 = 0 Δ = 25-112 = -87 nie ma rozwiązania [latex] left { {{x^2=8+y^2} atop {xy=3}} ight. [/latex] [latex] left { {{x=2√2+y} atop {(2√2+y)y=3}} ight. [/latex] [latex] left { {{x=2√2+y} atop {(2√2y+y^2=3}} ight. [/latex] y^2+2√2y-3=0 Δ=8+12=20 √Δ=2√5 y1 = [latex] frac{-2√2+2√5}{2} [/latex] = -√2+√5 y2 = [latex] frac{-2√2-2√5}{2} [/latex] = -√2-√5 x1 = 2√2-√2+√5 = √2+√5 x2 = 2√2-√2-√5 = √2-√5