题目内容
已知x,y
R,且|x+y|≤
, |x-y|≤
,求证:|5x+y|≤1.
因为|x+5y|=|3(x+y)+2(x-y)|.
由绝对值不等式性质,得
|x+5y|=|3(x+y)+2(x-y)|≤|3(x+y)|+|2(x-y)|
=3|x+y|+2|x-y|≤3×
+2×
=1.
即|x+5y|≤1.
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题目内容
已知x,y
R,且|x+y|≤
, |x-y|≤
,求证:|5x+y|≤1.
因为|x+5y|=|3(x+y)+2(x-y)|.
由绝对值不等式性质,得
|x+5y|=|3(x+y)+2(x-y)|≤|3(x+y)|+|2(x-y)|
=3|x+y|+2|x-y|≤3×
+2×
=1.
即|x+5y|≤1.