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kelya2
@kelya2
January 2021
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Pour demain , l'exercice numéro 2 un prombleme de math svp .. Merci d'avance
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AhYan
Verified answer
AB = 2x+1
AF = x+3
1) ABCD est un carré de côté 2x+1.
Or aire carré = côté²
Donc A(abcd) = (2x+1)²
ABEF est un rectangle. Or aire d'un rectangle = L×l
Donc A(abef) = (2x+1)(x+3)
2) A(fecd) = A(abcd) - A(abef)
A(fecd) = (2x+1)² - (2x+1)(x+3) = (2x+1)(2x+1-x-3)
A(fecd) = (2x+1)(x-2)
3) l = 2x+1
L = (2x+1)-(x+3) = 2x+1-x-3 = x-2
A(fecd) = (2x+1)×[(2x+1)-(x+3)]
4) A(fecd) = (2x+1)×[(2x+1)-(x+3)] = (2x+1)(2x+1-x-3) = (2x+1)(x-2)
5) On veut :
A(abcd) = 2×A(abef)
(2x+1)² = 2×(2x+1)(x+3)
(2x+1)² - 2×(2x+1)(x+3) = 0
(2x+1)[(2x+1)-2(x+3)] = 0
(2x+1)(2x+1-2x-6) = 0
(2x+1)×(-5) =0
-10x-5 = 0
-10x = 5
x = 5/-10 = -1/2
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Verified answer
AB = 2x+1AF = x+3
1) ABCD est un carré de côté 2x+1.
Or aire carré = côté²
Donc A(abcd) = (2x+1)²
ABEF est un rectangle. Or aire d'un rectangle = L×l
Donc A(abef) = (2x+1)(x+3)
2) A(fecd) = A(abcd) - A(abef)
A(fecd) = (2x+1)² - (2x+1)(x+3) = (2x+1)(2x+1-x-3)
A(fecd) = (2x+1)(x-2)
3) l = 2x+1
L = (2x+1)-(x+3) = 2x+1-x-3 = x-2
A(fecd) = (2x+1)×[(2x+1)-(x+3)]
4) A(fecd) = (2x+1)×[(2x+1)-(x+3)] = (2x+1)(2x+1-x-3) = (2x+1)(x-2)
5) On veut :
A(abcd) = 2×A(abef)
(2x+1)² = 2×(2x+1)(x+3)
(2x+1)² - 2×(2x+1)(x+3) = 0
(2x+1)[(2x+1)-2(x+3)] = 0
(2x+1)(2x+1-2x-6) = 0
(2x+1)×(-5) =0
-10x-5 = 0
-10x = 5
x = 5/-10 = -1/2