解決B(6)-A(6)=5000(1+46%/4)^24-5000(1+4.5%)^6 |Microsoft數學求解器

$$B ( 6 ) - A ( 6 ) = 5000 ( 1 + \frac { 46 \% } { 4 } ) ^ { 24 } - 5000 ( 1 + 4.5 \% ) ^ { 6 }$$

解 A

$$A=B-10275.7573661003795573605550886065096894916352618741902033984661102294921875$$

解線性方程式的步驟

透過找出與消去 2，對分式 \frac{46}{100} 約分至最低項。

$$B\times 6-A\times 6=5000\left(1+\frac{\frac{23}{50}}{4}\right)^{24}-5000\left(1+\frac{4.5}{100}\right)^{6}$$

運算式 \frac{\frac{23}{50}}{4} 為最簡分數。

$$B\times 6-A\times 6=5000\left(1+\frac{23}{50\times 4}\right)^{24}-5000\left(1+\frac{4.5}{100}\right)^{6}$$

將 50 乘上 4 得到 200。

$$B\times 6-A\times 6=5000\left(1+\frac{23}{200}\right)^{24}-5000\left(1+\frac{4.5}{100}\right)^{6}$$

將 1 與 \frac{23}{200} 相加可以得到 \frac{223}{200}。

$$B\times 6-A\times 6=5000\times \left(\frac{223}{200}\right)^{24}-5000\left(1+\frac{4.5}{100}\right)^{6}$$

計算 \frac{223}{200} 的 24 乘冪，然後得到 \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}。

$$B\times 6-A\times 6=5000\times \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}-5000\left(1+\frac{4.5}{100}\right)^{6}$$

將 5000 乘上 \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000} 得到 \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}。

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\left(1+\frac{4.5}{100}\right)^{6}$$

同時對分子與分母乘上 10 以展開 \frac{4.5}{100}。

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\left(1+\frac{45}{1000}\right)^{6}$$

透過找出與消去 5，對分式 \frac{45}{1000} 約分至最低項。

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\left(1+\frac{9}{200}\right)^{6}$$

將 1 與 \frac{9}{200} 相加可以得到 \frac{209}{200}。

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\times \left(\frac{209}{200}\right)^{6}$$

計算 \frac{209}{200} 的 6 乘冪，然後得到 \frac{83344647990241}{64000000000000}。

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\times \frac{83344647990241}{64000000000000}$$

將 5000 乘上 \frac{83344647990241}{64000000000000} 得到 \frac{83344647990241}{12800000000}。

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-\frac{83344647990241}{12800000000}$$

從 \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000} 減去 \frac{83344647990241}{12800000000} 會得到 \frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}。

$$B\times 6-A\times 6=\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}$$

將 -1 乘上 6 得到 -6。

$$B\times 6-6A=\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}$$

從兩邊減去 B\times 6。

$$-6A=\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-B\times 6$$

方程式為標準式。

$$-6A=\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-6B$$

將兩邊同時除以 -6。

$$\frac{-6A}{-6}=\frac{\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-6B}{-6}$$

除以 -6 可以取消乘以 -6 造成的效果。

$$A=\frac{\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-6B}{-6}$$

\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-6B 除以 -6。

$$A=B-\frac{68959440357862858206328969040580220826677637992671941547}{6710886400000000000000000000000000000000000000000000}$$

解 B

$$B=A+10275.7573661003795573605550886065096894916352618741902033984661102294921875$$

解線性方程式的步驟

透過找出與消去 2，對分式 \frac{46}{100} 約分至最低項。

$$B\times 6-A\times 6=5000\left(1+\frac{\frac{23}{50}}{4}\right)^{24}-5000\left(1+\frac{4.5}{100}\right)^{6}$$

運算式 \frac{\frac{23}{50}}{4} 為最簡分數。

$$B\times 6-A\times 6=5000\left(1+\frac{23}{50\times 4}\right)^{24}-5000\left(1+\frac{4.5}{100}\right)^{6}$$

將 50 乘上 4 得到 200。

$$B\times 6-A\times 6=5000\left(1+\frac{23}{200}\right)^{24}-5000\left(1+\frac{4.5}{100}\right)^{6}$$

將 1 與 \frac{23}{200} 相加可以得到 \frac{223}{200}。

$$B\times 6-A\times 6=5000\times \left(\frac{223}{200}\right)^{24}-5000\left(1+\frac{4.5}{100}\right)^{6}$$

計算 \frac{223}{200} 的 24 乘冪，然後得到 \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}。

$$B\times 6-A\times 6=5000\times \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}-5000\left(1+\frac{4.5}{100}\right)^{6}$$

將 5000 乘上 \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000} 得到 \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}。

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\left(1+\frac{4.5}{100}\right)^{6}$$

同時對分子與分母乘上 10 以展開 \frac{4.5}{100}。

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\left(1+\frac{45}{1000}\right)^{6}$$

透過找出與消去 5，對分式 \frac{45}{1000} 約分至最低項。

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\left(1+\frac{9}{200}\right)^{6}$$

將 1 與 \frac{9}{200} 相加可以得到 \frac{209}{200}。

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\times \left(\frac{209}{200}\right)^{6}$$

計算 \frac{209}{200} 的 6 乘冪，然後得到 \frac{83344647990241}{64000000000000}。

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-5000\times \frac{83344647990241}{64000000000000}$$

將 5000 乘上 \frac{83344647990241}{64000000000000} 得到 \frac{83344647990241}{12800000000}。

$$B\times 6-A\times 6=\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-\frac{83344647990241}{12800000000}$$

從 \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000} 減去 \frac{83344647990241}{12800000000} 會得到 \frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}。

$$B\times 6-A\times 6=\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}$$

新增 A\times 6 至兩側。

$$B\times 6=\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}+A\times 6$$

方程式為標準式。

$$6B=6A+\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}$$

將兩邊同時除以 6。

$$\frac{6B}{6}=\frac{6A+\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}}{6}$$

除以 6 可以取消乘以 6 造成的效果。

$$B=\frac{6A+\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}}{6}$$

\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}+6A 除以 6。

$$B=A+\frac{68959440357862858206328969040580220826677637992671941547}{6710886400000000000000000000000000000000000000000000}$$