算數(shù)平方根有意義,xy同號(hào).
x²+4y²+z²-3xy=2z√(xy)
x²+4y²+z²-2z√(xy)-3xy=0
x²-4xy+4y²+z²-2z√(xy)+xy=0
(x-2y)²+[z-√(xy)]=0
平方項(xiàng)恒非負(fù),兩平方項(xiàng)之和=0,兩平方項(xiàng)均=0
x-2y=0
z-√(xy)=0
解得x=2y z=√2|y|
y>0時(shí),z=√2 y
(x+y+z)/(2z-x)
=(2y+y+√2y)/[2(√2)y -2y]
=[(3+√2)y]/[(2√2-2)y]
=(3+√2)/(2√2-2)
=(3+√2)(2√2+2)/4
=(10+8√2)/4
=(5+4√2)/2
y