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rassoul11
@rassoul11
June 2021
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a > 0 et b > 0
Montrer que :
a/b + b/a > 2
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Bonjour
a/b + b/a > 2 équivalent
à a/b + b/a -2 > 0
équivalent (a²+b²-2ab)/ab>0
équivalent (a-b)²/ab>0
or (a-b)²>0
donc si a>0 et b>0, alors (a-b)²/ab>0
donc
a/b + b/a -2 > 0
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a/b + b/a > 2 équivalent à a/b + b/a -2 > 0
équivalent (a²+b²-2ab)/ab>0
équivalent (a-b)²/ab>0
or (a-b)²>0
donc si a>0 et b>0, alors (a-b)²/ab>0
donc a/b + b/a -2 > 0