Question

已知实数x,y满足x+2y+z=2根号x-1+4根号2y-6+2根号z+1,求x,y,z的值

Answer 1

左边=(x-1)+(2y-6)+(z+1)+6

将等式右边移到左边

√x-1（√x-1-2)+√2y-6(√2y-6-4)+√z+1（√z+1-2）+6=0

√x-1（√x-1-2)的最小值为-1 √ x-1=1 x=2

√2y-6(√2y-6-4)的最小值为-4 √2y-6=2 y=5

√z+1（√z+1-2）的最小值为-1 √z+1=1 z=0