Найдите значение x²-2xy+y² при х=3+√5, у=3-√5

[latex]x^2 - 2xy + y^2 = (x - y)^2 = (3 + \sqrt{5} - 3 + \sqrt{5})^2 = (2* \sqrt{5})^2 = 20[/latex]

[latex] x^{2} -2xy+ y^{2} = (x-y) ^{2}  \\  \\ (3+ \sqrt{5} - (3- \sqrt{5} ))^{2} = (3+ \sqrt{5} -3 + \sqrt{5} )^{2} = ( \sqrt{5} + \sqrt{5} ) ^{2} = (2* \sqrt{5} )^{2} \\ = 2 ^{2} * (\sqrt{5} ) ^{2} = 4 * 5 = 20[/latex] или [latex]=( \sqrt{5} + \sqrt{5}) ^{2} = ( \sqrt{5})^{2} + 2* \sqrt{5} * \sqrt{5} + ( \sqrt{5} ) ^{2}= 5+ 2 * ( \sqrt{5} )^{2}+ 5 = \\ = 5+2*5+5=5+10+5=20 [/latex]