Question

一道高中数学题，能告诉我为什么选c吗？谢谢各位

Answer 1

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Answer 2

结合长方体的对角线在三个面的投影来理解计算.如上图，

设长方体的长、宽、高分别为m、n、k，

由题意得√(m²+n²+k²)=√7，√(m²+k²)=√6 

∴n=1,√(1+k²)=a，√(1+m²)=b，

∴(a²-1)+(b²-1)=6，

∴出a²+b²=8，

∴(a+b)²=a²+2ab+b²=8+2ab≤8+a²+b²=16

 ∴a+b≤4，当且仅当a=b=2时取等号。

Answer 3

把这条棱放在三维坐标系xyz中，其中棱的一个端点不妨放在坐标原点，另一端点为P(x,y,z)，则由题目有
√(x^2+y^2+z^2)=√7
且√(x^2+y^2)=√6
因此z^2=1，不妨z=1
此时可知 x^2+y^2=√6
且a=√(x^2+1)，b=√(y^2+1)
因此a+b=√(x^2+1)+√(y^2+1)<=4
当且仅当x=y时，a+b=4
此时x=y=√3

Answer 4

额。。。脖子看歪了。。