Mccoy Davies
09/30/2023 · Elementary School
Exercice \( N^{0} 13: \) Soit \( A=A=2+3 \sqrt{5} \) er \( B=2-3 \sqrt{5} \) 1. Calculer \( A^{2} ; B^{2} A \times B \) 2. Démontrer que \( C=\frac{A}{B}+\frac{1}{4} \) est un nombre rationnel
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1. Calculons \( A^2 \), \( B^2 \) et \( A \times B \).
- \( A^2 = 49 + 12\sqrt{5} \)
- \( B^2 = 49 - 12\sqrt{5} \)
- \( A \times B = -41 \)
2. Démontrons que \( C = \frac{A}{B} + \frac{1}{4} \) est un nombre rationnel.
- \( C = -\frac{155}{164} \) est un nombre rationnel.
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