Exercice 1. 1 √2−√3 √2 : 2+ 3) × 4 3 √2 √ √ √ √3 𝑃=( 𝑃 = − 12 𝑄 = −2√48 + 3√192 − 4√75 𝑄 𝑎√𝑏(𝑎 ∈ ℤ; 𝑏 ∈ ℕ) 𝑄 𝑃 𝑄 𝑃(𝑃 − 1) = 𝑃−1 𝑄 Exercice 2. 𝐴 = (√5 − √3)2 𝐵 = 𝑥 2 − 7𝑥 + 10 𝐴 1 𝐶 = (√5 − √8 − 2√15) 2 𝐵 𝒙 = √2 Exercice 3. 𝑥 𝑦 𝑥 = 2√50 − 3√18 + √200 − √2 𝑦 = √20 + √80 − √32 √12 × √48 𝑚 = 1 − 2√3 𝑚 𝑛2 𝑚2 + 𝑛2 2 𝑝= Exercice 4. 𝑚 𝑛 𝑎√𝑏 𝑛 = 1 + √12 𝑚 + 𝑛, 𝑚 × 𝑛 𝑝 𝑎 𝑏 𝐺 = 76 − 2 37 − √ √ 𝐴𝐵𝐶 21 1 √ 9 + × 6 + √103 − 2√ 25 25 4 √ 𝐴 𝐴𝐵2 𝐴𝐶 = √3 − 1 𝐵𝐶 = 2√2 𝐴𝐵 = √3 + 1 𝐴𝐵𝐶 1 𝐴𝐶 Exercice 5. b (𝑎 ≠ 0 (𝑎2 𝑏−2 ) −5 𝐹 = ((𝑎3 )2 𝑏−4 )−2 𝑏 ≠ 0) ; 𝐹 = (𝑎𝑏)2 𝑎 = 5 × 10−5 𝑏 = 1015 𝐹 𝐹 𝑎 −𝑛 𝑎𝑛 𝑏−𝑎𝑛+1 𝐴 = 𝑏𝑛𝑎−𝑏𝑛+1 × (𝑏) 𝐴 𝑛 𝑎 ≠ 𝑏; 𝑎 ≠ 1; 𝑎 ≠ −1 Exercice 6. 1 √1+√2 + 1 √2+√3 + 1 √3+√4 + ⋯+ 1 √99+√100 1 1 2 1 1 = 9 ; (1 + 𝑛 − 𝑛+1) = 1 + 𝑛2 + (𝑛+1)2 (𝑛