Question

已知x=2减根号3y=2加根号3求下列代数式的值 x-y分之x乘根号y+y乘根号x 乘 根号x减根号y

Answer 1

你要求的是(1) x-(x√y ÷y)+y√x (2) √x-√y x=2-√3 y=2+√3 y>x
首先求（2）（√x-√y）²=x+y-2√xy=√2,所以= -√2
（1）可化为x-(x ÷√y)+y√x
括号中式子分子分母乘√x 可化为 x-(x√x ÷√y√x)+y√x
括号中√y√x带入x、y值后可化为x-x√x+y√x x-√y√x(√x-√y) =x+√2=2+√2-√3

Answer 2

x=2-√3 y=2+√3
(x√y+y√x)/(x-y)*(√x-√y)
=(x√y+y√x)*(√x-√y)/(x-y)
=[x√(xy)+xy-xy-y√(xy)]/(x-y)
=[x√(xy)-y√(xy)]/(x-y)
=[√(xy)(x-y)]/(x-y)
=√(xy)
=√(2-√3)(2+√3)
=√(4-3)
=√1
=1