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> 已知x,y,z满足(1)求170x+170y﹣28的值;(2)当x,y,z为何值时,有最大值?并求出此时的最大值。-八年级数学
已知x,y,z满足(1)求170x+170y﹣28的值;(2)当x,y,z为何值时,有最大值?并求出此时的最大值。-八年级数学
题目简介
已知x,y,z满足(1)求170x+170y﹣28的值;(2)当x,y,z为何值时,有最大值?并求出此时的最大值。-八年级数学
题目详情
已知x,y,z满足
(1)求170x+170y﹣28的值;
(2)当x,y,z为何值时,
有最大值?并求出此时的最大值。
题型:解答题
难度:中档
来源:广东省竞赛题
答案
解:(1)①×2+②,得3x+3y=36,
∴x+y=12,
∴170x+170y﹣28=170(x+y)﹣28=170×12﹣28=2012;
(2)由
得x+y=12,y﹣z=3,
∴x=12﹣y,z=y﹣3,
∴x2+y2+z2=(144﹣24y+y2)+y2+(y2﹣6y+9)=3y2﹣30y+153=3(y﹣5)2+78≥78,
当x2+y2+z2=78时,
有最大值,最大值为
=1,此时y=5,x=7,z=2。
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题目简介
已知x,y,z满足(1)求170x+170y﹣28的值;(2)当x,y,z为何值时,有最大值?并求出此时的最大值。-八年级数学
题目详情
(1)求170x+170y﹣28的值;
(2)当x,y,z为何值时,
答案
∴x+y=12,
∴170x+170y﹣28=170(x+y)﹣28=170×12﹣28=2012;
(2)由
得x+y=12,y﹣z=3,
∴x=12﹣y,z=y﹣3,
∴x2+y2+z2=(144﹣24y+y2)+y2+(y2﹣6y+9)=3y2﹣30y+153=3(y﹣5)2+78≥78,
当x2+y2+z2=78时,