Niech x+y=12 i x^2+y^2=126 Oblicz wartosc wyrazenia x*y

[latex]x+y=12\(x+y)^2=12^2\x^2+2xy+y^2=144\126+2xy=144\2xy=18\xy=9[/latex]

[latex]\(x+y)^2=x^2+2xy+y^2 \ \x^2+y^2=(x+y)^2-2xy \ \2xy=(x+y)^2-(x^2+y^2) \ \xy=frac12*[(x+y)^2-(x^2+y^2)]=frac12*(12^2-126)=frac12(144-126) \ \xy=frac12*18=9[/latex]