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Smades
@Smades
May 2019
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Bonjour, pouvez-vous m’aider ?
Cordialement.
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Volume cube = x³
volume pavé droit = (x-20)(x+20)²
= (x-20)(x²+40x+400)
= x³+40x²+400x-20x²-800x-8000
= 20x²-400x-8000
= x³+x²-20x-400
1) volume cube ≥ volume pavé droit
⇒ x³ ≥ x³+x²-20x-400
⇒ x³-x³ ≥ x²-20x-400
⇒ 0 ≥ x²-20x-400
⇒ x²-20x-400 ≤ 0
2) (x -10)² - 500 = x²-20x+100-500 = x²-20x-400
3) x²-20x-400 ≤ 0
⇒ (x -10)² - 500 ≤ 0
⇒ (x -10)² ≤ 500
⇒ x-10 ≤ √500 ou x-10 ≤ -√500
⇒ x ≤ 10+√500 ou x ≤ 10-√500
L'énoncé nous dit que x > 20.
Il ne reste donc qu'une solution : x ≤ 10+√500
donc : x ≤ 10 + √(10²×5)
x ≤ 10 + 10√5
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Bonsoir, aidez-moi svp, merci. Cordialement Smades
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Lista de comentários
volume pavé droit = (x-20)(x+20)²
= (x-20)(x²+40x+400)
= x³+40x²+400x-20x²-800x-8000
= 20x²-400x-8000
= x³+x²-20x-400
1) volume cube ≥ volume pavé droit
⇒ x³ ≥ x³+x²-20x-400
⇒ x³-x³ ≥ x²-20x-400
⇒ 0 ≥ x²-20x-400
⇒ x²-20x-400 ≤ 0
2) (x -10)² - 500 = x²-20x+100-500 = x²-20x-400
3) x²-20x-400 ≤ 0
⇒ (x -10)² - 500 ≤ 0
⇒ (x -10)² ≤ 500
⇒ x-10 ≤ √500 ou x-10 ≤ -√500
⇒ x ≤ 10+√500 ou x ≤ 10-√500
L'énoncé nous dit que x > 20.
Il ne reste donc qu'une solution : x ≤ 10+√500
donc : x ≤ 10 + √(10²×5)
x ≤ 10 + 10√5