cho `1 ≤x

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cho `1 ≤x

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Adalyn 1 tháng 2021-08-06T22:15:25+00:00 1 Answers 2 views 0

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    2021-08-06T22:16:43+00:00

    ta có :

    ` 1≤x<y≤2`

    `⇒y≤2x`

    `⇒2x-y≥0`

    mà` x<y`

    `⇒x-2y<0`

    `⇒(2x-y)(x-2y)≤0`

    `⇒2x^2-xy-4xy+2y^2≤0`

    `⇒2x^2+2y^2≤5xy`

    `⇒x^2+y^2≤5/2 xy`

    `⇒x/y+y/x≤5/2`

    đặt 

    `A=(x+y)(1/x +1/y)`

    `⇒A=2+x/y+y/x`

    `⇒5/2+2≥A`

    `⇔2,5≥A`

    dấu `”=”` xẩy ra khi:

    `x=1 ;y=2`

    vậy `max=2,5` khi `x=1 ;y=2`

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