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:800 ℃时间:2020-07-27 12:16:51
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...
我来回答
类似推荐
猜你喜欢
- 1初中数学哪块是重点哪块比较难
- 2如图,在三角形ABC中,BP、CP分别是∠ABC、∠ACB的外角平分线.求证:点P必在∠A的平分线上.
- 3我们在挫折中成长 作文
- 4作文“感恩父母,要1000字,
- 5我必须警告你不要出去,暴风雨要来了. 翻译成英文用到warn...not to do.急用啊谢谢大家啦
- 63.3KN/M等于多少LBS/IN
- 7我们生活的地球是个球体 对还是错
- 812x-9x=8.7 怎么解方程
- 9Kuming is_____ city that thousands of people visit it every day.
- 10This is my family name?HI,---------- A Brown BWhite C Harry D Tom