Question

已知X>2,求函数Y=3X+6/(X-2)的最小值？并指出X的值 谢谢

Answer 1

X>2,则x-2>0
函数Y=3X+6/(X-2)=3(x-2)+6/(x-2)+6>=2根号[3(x-2)*6/(x-2)]+6=6根号2+6
当3(x-2)=6/(x-2),即x=2+根号2时,取"="
所以,当x=2+根号2时,最小值是:6根号2+6

Answer 2

y=3x-6+6+6/(x-2)
=3(x-2)+6/(x-2)+6
x>2则x-2>0
所以3(x-2)+6/(x-2)+6≥2√[3(x-2)*6/(x-2)]+6=6√2+6
当3(x-2)=6/(x-2)时取等号
(x-2)²=2
x=2+√2
所以
x=2+√2，y最小=6√2+6