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Cho a> 0 . Tìm giá trị nhỏ nhất của biểu thức P `= (2a^2+3a+8)/a`

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StarButterflyy

7 tháng trước

Đáp án:

Giải thích các bước giải:

`P= (2a^2 + 3a + 8)/a`

`P= (2a^2)/a + (3a)/a + 8/a`

`P= 2a + 3 + 8/a`

`P= 2a + 8/a +3`

Áp dụng BĐT cô si ta có:

`P= 2a + 8/a +3≥ 2 \sqrt{2a . 8/a} +3 = 2 . \sqrt{16} +3 = 11`

Dấu `"="` xảy ra `<=> 2a = 8/a`

`<=> 2a^2 = 8`

`<=> a^2 = 4`

`<=> a= ±2`

Mà `a > 0`

`=> a = 2`

Vậy Min `P = 11` khi và chỉ khi `a=2`

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Choose the best answer.
We should decorate our living room with _ orange banner. We also need ____ ribbons, balloons, party hats and costume.

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