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

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

Решаване за A

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

Стъпки за решаване на линейно уравнение

Намаляване на дробта \frac{46}{100} до най-малките членове чрез извличане на корен и съкращаване на 2.

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

Изразете \frac{\frac{23}{50}}{4} като една дроб.

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

Умножете 50 по 4, за да получите 200.

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

Съберете 1 и \frac{23}{200}, за да се получи \frac{223}{200}.

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

Изчислявате 24 на степен \frac{223}{200} и получавате \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}.

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

Умножете 5000 по \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}, за да получите \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}.

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

Намаляване на дробта \frac{45}{100} до най-малките членове чрез извличане на корен и съкращаване на 5.

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

Съберете 1 и \frac{9}{20}, за да се получи \frac{29}{20}.

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

Изчислявате 6 на степен \frac{29}{20} и получавате \frac{594823321}{64000000}.

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

Умножете 5000 по \frac{594823321}{64000000}, за да получите \frac{594823321}{12800}.

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

Извадете \frac{594823321}{12800} от \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}, за да получите \frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}.

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

Умножете -1 по 6, за да получите -6.

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

Извадете B\times 6 и от двете страни.

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

Уравнението е в стандартна форма.

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

Разделете двете страни на -6.

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

Делението на -6 отменя умножението по -6.

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

Разделете \frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-6B на -6.

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

Решаване за B

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

Стъпки за решаване на линейно уравнение

Намаляване на дробта \frac{46}{100} до най-малките членове чрез извличане на корен и съкращаване на 2.

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

Изразете \frac{\frac{23}{50}}{4} като една дроб.

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

Умножете 50 по 4, за да получите 200.

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

Съберете 1 и \frac{23}{200}, за да се получи \frac{223}{200}.

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

Изчислявате 24 на степен \frac{223}{200} и получавате \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}.

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

Умножете 5000 по \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}, за да получите \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}.

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

Намаляване на дробта \frac{45}{100} до най-малките членове чрез извличане на корен и съкращаване на 5.

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

Съберете 1 и \frac{9}{20}, за да се получи \frac{29}{20}.

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

Изчислявате 6 на степен \frac{29}{20} и получавате \frac{594823321}{64000000}.

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

Умножете 5000 по \frac{594823321}{64000000}, за да получите \frac{594823321}{12800}.

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

Извадете \frac{594823321}{12800} от \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}, за да получите \frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}.

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

Добавете A\times 6 от двете страни.

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

Уравнението е в стандартна форма.

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

Разделете двете страни на 6.

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

Делението на 6 отменя умножението по 6.

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

Разделете \frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}+6A на 6.

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