Ch14 23
- 1. Exercice 23 (a) log(xy) = 3 log x = 1 y xy = 103 = 1000 1 x y = 101 = 10 2 De la seconde équation on tire : x = 10y. L’équation 1 devient : (10y) · y = 1000 10y2 = 1000 y = 10 y2 = 100 y = −10
- 2. Exercice 23 (suite..) x • Si y = 10 → = 10 → x = 100 10 x • Si y = −10 → = 10 → x = −100 −10 S = {(x = 100; y = 10); (x = −100; y = −10)} (b) log(x) + log(y) = 2 x + y = 25 log(xy) = 2 x + y = 25 xy = 102 = 100 x + y = 25
- 3. Exercice 23 (suite..) x = 25 − y que l’on remplace dans la première équation : (25 − y)y = 100 − y2 + 25y = 100 y = 20 y2 − 25y + 100 = 0 y=5 • Si y = 20 → x = 25 − 20 = 5 • Si y = 5 → x = 25 − 5 = 20 S = {(x = 5; y = 20); (x = 20; y = 5)}