Chung minh: ║ ║x ║- ║y ║ ║ ≤ ║x-y ║ ║la gia tri tuyet doi ║ ║la gia tri tuyet doi cua gia tri tuyet doi 03/12/2021 Bởi Vivian Chung minh: ║ ║x ║- ║y ║ ║ ≤ ║x-y ║ ║la gia tri tuyet doi ║ ║la gia tri tuyet doi cua gia tri tuyet doi
Ta có: $| |x| – |y| | ≤ |x-y|$ $⇔ |x – y| ≤ |x-y|$ $⇔ |x – y| = |x-y| $⇔ | |x| – |y| | ≤ |x-y|$ Bình luận
║ ║x ║- ║y ║ ║ ≤ ║x-y ║ <=> ║ x – y ║ ≤ ║x-y ║ <=> ║ x – y ║ = ║x-y ║ => ║ ║x ║- ║y ║ ║ = ║x-y ║ Bình luận
Ta có:
$| |x| – |y| | ≤ |x-y|$
$⇔ |x – y| ≤ |x-y|$
$⇔ |x – y| = |x-y|
$⇔ | |x| – |y| | ≤ |x-y|$
║ ║x ║- ║y ║ ║ ≤ ║x-y ║
<=> ║ x – y ║ ≤ ║x-y ║
<=> ║ x – y ║ = ║x-y ║
=> ║ ║x ║- ║y ║ ║ = ║x-y ║