若x,y,z均为非负数,且满足x−1=y+1/2=z−23,则x2+y2+z2可取得的最小值为_.
若x,y,z均为非负数,且满足x−1=
=
,则x2+y2+z2可取得的最小值为______.
y+1 |
2 |
z−2 |
3 |
数学人气:523 ℃时间:2020-03-25 15:50:03
优质解答
令x-1=y+12=z−23=t,则x=t+1,y=2t-1,z=3t+2,于是x2+y2+z2=(t+1)2+(2t-1)2+(3t+2)2=t2+2t+1+4t2+1-4t+9t2+4+12t=14t2+10t+6,∵x,y,z均为非负数,∴x-1≥-1,y+12≥12,z−23≥-23,∵x-1=y+12=t,∴y≥1...
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