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

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

Lahendage ja leidke A

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

Juhised lineaarvõrrandi lahendamiseks

Taandage murd \frac{46}{100} vähimale ühiskordsele, eraldades ja taandades arvu 2.

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

Avaldage \frac{\frac{23}{50}}{4} ühe murdarvuna.

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

Korrutage 50 ja 4, et leida 200.

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

Liitke 1 ja \frac{23}{200}, et leida \frac{223}{200}.

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

Arvutage 24 aste \frac{223}{200} ja leidke \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}.

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

Korrutage 5000 ja \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}, et leida \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}.

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

Taandage murd \frac{45}{100} vähimale ühiskordsele, eraldades ja taandades arvu 5.

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

Liitke 1 ja \frac{9}{20}, et leida \frac{29}{20}.

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

Arvutage 6 aste \frac{29}{20} ja leidke \frac{594823321}{64000000}.

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

Korrutage 5000 ja \frac{594823321}{64000000}, et leida \frac{594823321}{12800}.

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

Lahutage \frac{594823321}{12800} väärtusest \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}, et leida \frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}.

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

Korrutage -1 ja 6, et leida -6.

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

Lahutage mõlemast poolest B\times 6.

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

Võrrand on standardkujul.

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

Jagage mõlemad pooled -6-ga.

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

-6-ga jagamine võtab -6-ga korrutamise tagasi.

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

Jagage \frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-6B väärtusega -6.

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

Lahendage ja leidke B

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

Juhised lineaarvõrrandi lahendamiseks

Taandage murd \frac{46}{100} vähimale ühiskordsele, eraldades ja taandades arvu 2.

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

Avaldage \frac{\frac{23}{50}}{4} ühe murdarvuna.

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

Korrutage 50 ja 4, et leida 200.

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

Liitke 1 ja \frac{23}{200}, et leida \frac{223}{200}.

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

Arvutage 24 aste \frac{223}{200} ja leidke \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}.

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

Korrutage 5000 ja \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}, et leida \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}.

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

Taandage murd \frac{45}{100} vähimale ühiskordsele, eraldades ja taandades arvu 5.

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

Liitke 1 ja \frac{9}{20}, et leida \frac{29}{20}.

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

Arvutage 6 aste \frac{29}{20} ja leidke \frac{594823321}{64000000}.

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

Korrutage 5000 ja \frac{594823321}{64000000}, et leida \frac{594823321}{12800}.

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

Lahutage \frac{594823321}{12800} väärtusest \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}, et leida \frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}.

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

Liitke A\times 6 mõlemale poolele.

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

Võrrand on standardkujul.

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

Jagage mõlemad pooled 6-ga.

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

6-ga jagamine võtab 6-ga korrutamise tagasi.

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

Jagage \frac{72797255816118311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}+6A väärtusega 6.

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