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sisi32
@sisi32
January 2021
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Pourriez vous m'expliquez comment a été trouvé le résultat de A-G c'est à dire 1/2(√a-√b)²≥0
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gilles2016
A= a+b / 2 et G= √ab
A-G=a+b / 2-
√ab
= (a+b-2
√ab)/2 or a+b-2√ab=(√a)²-2√ab+(√b)²=(√a)²-2√a×√b+(
√b)²
= [
(√a)²-2√a×√b+(
√b)²]/2
= (
√a-√b)² / 2 car (√a)²-2√a×√b+(
√b)²=(
√a-√b)² ( identité remarquable a²-2ab+b²=(a-b)² )
Bon courage !
1 votes
Thanks 1
lota50
Les identites remarquables !(A-B)² = A²+B²-2AB
1 votes
Thanks 1
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A-G=a+b / 2- √ab
= (a+b-2√ab)/2 or a+b-2√ab=(√a)²-2√ab+(√b)²=(√a)²-2√a×√b+(√b)²
= [(√a)²-2√a×√b+(√b)²]/2
= (√a-√b)² / 2 car (√a)²-2√a×√b+(√b)²=(√a-√b)² ( identité remarquable a²-2ab+b²=(a-b)² )
Bon courage !