已知x+y-2√x-4√y+5=0,求实数xy的值

问题描述:

已知x+y-2√x-4√y+5=0,求实数xy的值

x +y-2√x-4√y+5=0
(√x)²+(√y)²-2√x-4√y+5=0
(√x)²-2√x+1+(√y)²-4√y+4=0
(√x-1)²+(√y-2)²=0
(√x-1)²=0 (√y-2)²=0
√x=1 √y=2
x=1 y=4
xy=4