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Hà Minh Hiếu 27/02/2018 at 11:09A = \(\left(1-\dfrac{4}{a^2}\right)\left(1-\dfrac{4}{b^2}\right)\)
= \(\dfrac{\left(a-2\right)\left(a+2\right)\left(b-2\right)\left(b+2\right)}{a^2b^2}\)
= \(\dfrac{ab\left(a+2\right)\left(b+2\right)}{a^2b^2}\)
= \(\dfrac{ab+2\left(a+b\right)+4}{ab}\)
= \(1+\dfrac{8}{ab}\)
\(\le1+\dfrac{8}{\left(\dfrac{a+b}{2}\right)^2}=1+8=9\)
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Thanh Nguyen 07/02/2018 at 19:18
9 . cá 100%
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Faded 22/01/2018 at 12:33A= (1-2a)(1-2b)(1+2a)(1+2b
)
A= ( 1-a+ba
)(1-a+bb)(1+a+ba)(1+a+bb
)
A= ba
.ab.(2+ba)(2+ab
)
A= 4 +1 + 2 (ba+ab
) >= 5 +2. 2√ba.ab= 5+4 =9
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Ngô Phương 08/01/2018 at 16:47A= (1-\(\dfrac{2}{a}\))(1-\(\dfrac{2}{b}\))(1+\(\dfrac{2}{a}\))(1+\(\dfrac{2}{b}\))
A= ( 1-\(\dfrac{a+b}{a}\))(1-\(\dfrac{a+b}{b}\))(1+\(\dfrac{a+b}{a}\))(1+\(\dfrac{a+b}{b}\))
A= \(\dfrac{b}{a}\).\(\dfrac{a}{b}\).(2+\(\dfrac{b}{a}\))(2+\(\dfrac{a}{b}\))
A= 4 +1 + 2 (\(\dfrac{b}{a}+\dfrac{a}{b}\)) >= 5 +2. 2\(\sqrt{\dfrac{b}{a}.\dfrac{a}{b}}\)= 5+4 =9