Oblicz wartość liczbową wyrażenia [latex]2(3x-y) ^{2} -3(2x+y)(y-2x)+12xy [/latex] dla [latex]x= sqrt{2} [/latex] ; [latex]y= -3 sqrt6} [/latex].

[latex]2(3x-y) ^{2} -3(2x+y)(y-2x)+12xy =\=18x^2-12xy+2y^2-3y^2+12x^2+12xy=\=30x^2-y^2 = 30cdot (sqrt{2})^2-(-3sqrt{6})^2 = 60 - 54=6[/latex]

[latex] 2(3x-y)^2-3(2x+y)(y-2x)+12xy =\\=2(9x^2-6xy+y^2)+3(2x+y)(2x-y)+12xy=\\=18x^2-12xy+2y^2 +3(4x^2-y^2) +12xy\\=18x^2-12xy+2y^2 +12x^2-3y^2 +12xy =30x^2-y^2 \\ x= sqrt{2}, y= -3 sqrt{6} \\ 30x^2-y^2=30 cdot (sqrt{2})^2- (-3sqrt{6})^2=30cdot 2 -9 cdot 6=60-54=6[/latex]