Résoudre B(6)-A(6)=5000(1+46%/4)^24-5000(1+45%)^6

$$B ( 6 ) - A ( 6 ) = 5000 ( 1 + \frac { 46 \% } { 4 } ) ^ { 24 } - 5000 ( 1 + 45 \% ) ^ { 6 }$$

Calculer A

$$A = -\frac{24265751938706103774328969040580220826677637992671941547}{6710886400000000000000000000000000000000000000000000} = -3615\frac{5,897602706102325 \times 10^{51}}{6,710886400000001 \times 10^{51}} = -3615,878811285809$$

Étapes de calcul des équations linéaires

Réduire la fraction \frac{46}{100} au maximum en extrayant et en annulant 2.

$$B\times 6-A\times 6=5000\left(1+\frac{\frac{23}{50}}{4}\right)^{24}-5000\left(1+\frac{45}{100}\right)^{6}$$

Exprimer \frac{\frac{23}{50}}{4} sous la forme d’une fraction seule.

$$B\times 6-A\times 6=5000\left(1+\frac{23}{50\times 4}\right)^{24}-5000\left(1+\frac{45}{100}\right)^{6}$$

Multiplier 50 et 4 pour obtenir 200.

$$B\times 6-A\times 6=5000\left(1+\frac{23}{200}\right)^{24}-5000\left(1+\frac{45}{100}\right)^{6}$$

Additionner 1 et \frac{23}{200} pour obtenir \frac{223}{200}.

$$B\times 6-A\times 6=5000\times \left(\frac{223}{200}\right)^{24}-5000\left(1+\frac{45}{100}\right)^{6}$$

Calculer \frac{223}{200} à la puissance 24 et obtenir \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}.

$$B\times 6-A\times 6=5000\times \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}-5000\left(1+\frac{45}{100}\right)^{6}$$

Multiplier 5000 et \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000} pour obtenir \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}.

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\left(1+\frac{45}{100}\right)^{6}$$

Réduire la fraction \frac{45}{100} au maximum en extrayant et en annulant 5.

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\left(1+\frac{9}{20}\right)^{6}$$

Additionner 1 et \frac{9}{20} pour obtenir \frac{29}{20}.

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\times \left(\frac{29}{20}\right)^{6}$$

Calculer \frac{29}{20} à la puissance 6 et obtenir \frac{594823321}{64000000}.

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\times \frac{594823321}{64000000}$$

Multiplier 5000 et \frac{594823321}{64000000} pour obtenir \frac{594823321}{12800}.

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-\frac{594823321}{12800}$$

Soustraire \frac{594823321}{12800} de \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000} pour obtenir \frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}.

$$B\times 6-A\times 6=\frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}$$

Multiplier -1 et 6 pour obtenir -6.

$$B\times 6-6A=\frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}$$

Soustraire B\times 6 des deux côtés.

$$-6A=\frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-B\times 6$$

L’équation utilise le format standard.

$$-6A=\frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-6B$$

Divisez les deux côtés par -6.

$$\frac{-6A}{-6}=\frac{\frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-6B}{-6}$$

La division par -6 annule la multiplication par -6.

$$A=\frac{\frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-6B}{-6}$$

Diviser \frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-6B par -6.

$$A=B-\frac{24265751938706103774328969040580220826677637992671941547}{6710886400000000000000000000000000000000000000000000}$$

Calculer B

$$B = \frac{24265751938706103774328969040580220826677637992671941547}{6710886400000000000000000000000000000000000000000000} = 3615\frac{5,897602706102325 \times 10^{51}}{6,710886400000001 \times 10^{51}} = 3615,878811285809$$

Étapes de calcul des équations linéaires

Réduire la fraction \frac{46}{100} au maximum en extrayant et en annulant 2.

$$B\times 6-A\times 6=5000\left(1+\frac{\frac{23}{50}}{4}\right)^{24}-5000\left(1+\frac{45}{100}\right)^{6}$$

Exprimer \frac{\frac{23}{50}}{4} sous la forme d’une fraction seule.

$$B\times 6-A\times 6=5000\left(1+\frac{23}{50\times 4}\right)^{24}-5000\left(1+\frac{45}{100}\right)^{6}$$

Multiplier 50 et 4 pour obtenir 200.

$$B\times 6-A\times 6=5000\left(1+\frac{23}{200}\right)^{24}-5000\left(1+\frac{45}{100}\right)^{6}$$

Additionner 1 et \frac{23}{200} pour obtenir \frac{223}{200}.

$$B\times 6-A\times 6=5000\times \left(\frac{223}{200}\right)^{24}-5000\left(1+\frac{45}{100}\right)^{6}$$

Calculer \frac{223}{200} à la puissance 24 et obtenir \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}.

$$B\times 6-A\times 6=5000\times \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}-5000\left(1+\frac{45}{100}\right)^{6}$$

Multiplier 5000 et \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000} pour obtenir \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}.

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\left(1+\frac{45}{100}\right)^{6}$$

Réduire la fraction \frac{45}{100} au maximum en extrayant et en annulant 5.

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\left(1+\frac{9}{20}\right)^{6}$$

Additionner 1 et \frac{9}{20} pour obtenir \frac{29}{20}.

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\times \left(\frac{29}{20}\right)^{6}$$

Calculer \frac{29}{20} à la puissance 6 et obtenir \frac{594823321}{64000000}.

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\times \frac{594823321}{64000000}$$

Multiplier 5000 et \frac{594823321}{64000000} pour obtenir \frac{594823321}{12800}.

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-\frac{594823321}{12800}$$

Soustraire \frac{594823321}{12800} de \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000} pour obtenir \frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}.

$$B\times 6-A\times 6=\frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}$$

Ajouter A\times 6 aux deux côtés.

$$B\times 6=\frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}+A\times 6$$

L’équation utilise le format standard.

$$6B=6A+\frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}$$

Divisez les deux côtés par 6.

$$\frac{6B}{6}=\frac{6A+\frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}}{6}$$

La division par 6 annule la multiplication par 6.

$$B=\frac{6A+\frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}}{6}$$

Diviser \frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}+6A par 6.

$$B=A+\frac{24265751938706103774328969040580220826677637992671941547}{6710886400000000000000000000000000000000000000000000}$$