若x-1=(y+1)/2=(z-2)/3,求x^2+y^2+z^2的最小值 配方法一定要用配方法
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若x-1=(y+1)/2=(z-2)/3,求x^2+y^2+z^2的最小值配方法一定要用配方法若x-1=(y+1)/2=(z-2)/3,求x^2+y^2+z^2的最小值配方法一定要用配方法若x-1=(
若x-1=(y+1)/2=(z-2)/3,求x^2+y^2+z^2的最小值 配方法一定要用配方法
若x-1=(y+1)/2=(z-2)/3,求x^2+y^2+z^2的最小值 配方法
一定要用配方法
若x-1=(y+1)/2=(z-2)/3,求x^2+y^2+z^2的最小值 配方法一定要用配方法
答:
设x-1=(y+1)/2=(z-2)/3=k
解得:
x=k+1
y=2k-1
z=3k+2
所以:
x²+y²+z²
=(k+1)²+(2k-1)²+(3k+2)²
=k²+2k+1+4k²-4k+1+9k²+12k+4
=14k²+10k+6
=14*(k²+2*5k/14+25/196)-25/14+6
=14*(k+5/14)²+59/14
当k+5/14=0时,取得最小值59/14
所以:x²+y²+z²的最小值为59/14
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