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DEVOIR B - Semestre 1 - 3APIC Dr. Karam Ouharou .pdf
1.
. 1 Exercice 𝑃 = ( √2−√3 √2 : 1 √2+√3 )
× √2 4√3 𝑃 = − √3 12 𝑄 = −2√48 + 3√192 − 4√75 𝑄 𝑎√𝑏(𝑎 ∈ ℤ; 𝑏 ∈ ℕ) 𝑄 𝑃 𝑄 𝑃(𝑃 − 1) = 𝑃−1 𝑄 . 2 Exercice 𝐴 = (√5 − √3)2 𝐵 = 𝑥2 − 7𝑥 + 10 𝐴 𝐶 = 1 2 (√5 − √8 − 2√15) 𝐵 𝒙 = √2 . 3 Exercice 𝑥 𝑦 𝑎√𝑏 𝑎 𝑏 𝑥 = 2√50 − 3√18 + √200 − √2 𝑦 = √20 + √80 − √32 √12 × √48 𝑚 = 1 − 2√3 𝑛 = 1 + √12 𝑚2 𝑛2 𝑚 + 𝑛, 𝑚 × 𝑛 𝑚2 + 𝑛2 𝑝 = 𝑚 𝑛 𝑝 . 4 Exercice
2.
𝐺 = √ 76 −
2 √ 37 − √ 21 25 + 1 25 × √6 + √103 − 2√ 9 4 𝐴𝐵𝐶 𝐴 𝐴𝐶 = √3 − 1 𝐵𝐶 = 2√2 𝐴𝐵2 𝐴𝐵 = √3 + 1 𝐴𝐵𝐶 1 𝐴𝐶 . 5 Exercice b (𝑎 ≠ 0 𝑏 ≠ 0) ; 𝐹 = (𝑎2𝑏−2) −5 ((𝑎3)2𝑏−4)−2 𝐹 = (𝑎𝑏)2 𝑎 = 5 × 10−5 𝑏 = 1015 𝐹 𝐹 𝐴 𝐴 = 𝑎𝑛𝑏−𝑎𝑛+1 𝑏𝑛𝑎−𝑏𝑛+1 × ( 𝑎 𝑏 ) −𝑛 𝑛 𝑎 ≠ 𝑏; 𝑎 ≠ 1; 𝑎 ≠ −1 . 6 Exercice 1 √1+√2 + 1 √2+√3 + 1 √3+√4 + ⋯ + 1 √99+√100 = 9 ; (1 + 1 𝑛 − 1 𝑛+1 ) 2 = 1 + 1 𝑛2 + 1 (𝑛+1)2 (𝑛
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