ដោះស្រាយ B(6)-A(6)=5000(1+46%/4)^24-5000(1+4.5%)^6

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

ដោះស្រាយសម្រាប់ A

$$A=B-10275.7573661003795573605550886065096894916352618741902033984661102294921875$$

ជំហានសម្រាប់ការដោះស្រាយសមីការលីនេអ៊ែរ

កាត់បន្ថយប្រភាគ \frac{46}{100} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 2។

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

បង្ហាញ \frac{\frac{23}{50}}{4} ជាប្រភាគទោល។

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

គុណ 50 និង 4 ដើម្បីបាន 200។

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

បូក 1 និង \frac{23}{200} ដើម្បីបាន \frac{223}{200}។

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

គណនាស្វ័យគុណ \frac{223}{200} នៃ 24 ហើយបាន \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}។

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

គុណ 5000 និង \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000} ដើម្បីបាន \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}។

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

ពង្រីក \frac{4.5}{100} ដោយគុណទាំងភាគបែង និងភាគយកជាមួយនឹង 10។

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

កាត់បន្ថយប្រភាគ \frac{45}{1000} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 5។

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

បូក 1 និង \frac{9}{200} ដើម្បីបាន \frac{209}{200}។

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

គណនាស្វ័យគុណ \frac{209}{200} នៃ 6 ហើយបាន \frac{83344647990241}{64000000000000}។

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

គុណ 5000 និង \frac{83344647990241}{64000000000000} ដើម្បីបាន \frac{83344647990241}{12800000000}។

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

ដក​ \frac{83344647990241}{12800000000} ពី \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000} ដើម្បីបាន \frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}។

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

គុណ -1 និង 6 ដើម្បីបាន -6។

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

ដក B\times 6 ពីជ្រុងទាំងពីរ។

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

សមីការឥឡូវនេះស្ថិតនៅក្នុងទម្រង់ស្ដង់ដារ។

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

ចែកជ្រុងទាំងពីនឹង -6។

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

ការចែកនឹង -6 មិនធ្វើប្រមាណវិធីគុណនឹង -6 ឡើងវិញ។

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

ចែក \frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-6B នឹង -6។

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

ដោះស្រាយសម្រាប់ B

$$B=A+10275.7573661003795573605550886065096894916352618741902033984661102294921875$$

ជំហានសម្រាប់ការដោះស្រាយសមីការលីនេអ៊ែរ

កាត់បន្ថយប្រភាគ \frac{46}{100} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 2។

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

បង្ហាញ \frac{\frac{23}{50}}{4} ជាប្រភាគទោល។

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

គុណ 50 និង 4 ដើម្បីបាន 200។

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

បូក 1 និង \frac{23}{200} ដើម្បីបាន \frac{223}{200}។

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

គណនាស្វ័យគុណ \frac{223}{200} នៃ 24 ហើយបាន \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}។

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

គុណ 5000 និង \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000} ដើម្បីបាន \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}។

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

ពង្រីក \frac{4.5}{100} ដោយគុណទាំងភាគបែង និងភាគយកជាមួយនឹង 10។

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

កាត់បន្ថយប្រភាគ \frac{45}{1000} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 5។

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

បូក 1 និង \frac{9}{200} ដើម្បីបាន \frac{209}{200}។

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

គណនាស្វ័យគុណ \frac{209}{200} នៃ 6 ហើយបាន \frac{83344647990241}{64000000000000}។

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

គុណ 5000 និង \frac{83344647990241}{64000000000000} ដើម្បីបាន \frac{83344647990241}{12800000000}។

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

ដក​ \frac{83344647990241}{12800000000} ពី \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000} ដើម្បីបាន \frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}។

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

បន្ថែម A\times 6 ទៅជ្រុងទាំងពីរ។

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

សមីការឥឡូវនេះស្ថិតនៅក្នុងទម្រង់ស្ដង់ដារ។

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

ចែកជ្រុងទាំងពីនឹង 6។

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

ការចែកនឹង 6 មិនធ្វើប្រមាណវិធីគុណនឹង 6 ឡើងវិញ។

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

ចែក \frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}+6A នឹង 6។

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