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

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

Ebatzi: A

$$A=B-10275.7573661003795573605550886065096894916352618741902033984661102294921875$$

Ekuazio lineala ebazteko urratsak

Murriztu \frac{46}{100} zatikia gai txikienera, 2 bakanduta eta ezeztatuta.

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

Adierazi \frac{\frac{23}{50}}{4} frakzio bakar gisa.

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

200 lortzeko, biderkatu 50 eta 4.

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

\frac{223}{200} lortzeko, gehitu 1 eta \frac{23}{200}.

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

\frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000} lortzeko, egin \frac{223}{200} ber 24.

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

\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000} lortzeko, biderkatu 5000 eta \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}.

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

Hedatu \frac{4.5}{100} zenbakitzailea eta izendatzailea 10 balioarekin biderkatuta.

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

Murriztu \frac{45}{1000} zatikia gai txikienera, 5 bakanduta eta ezeztatuta.

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

\frac{209}{200} lortzeko, gehitu 1 eta \frac{9}{200}.

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

\frac{83344647990241}{64000000000000} lortzeko, egin \frac{209}{200} ber 6.

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

\frac{83344647990241}{12800000000} lortzeko, biderkatu 5000 eta \frac{83344647990241}{64000000000000}.

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

\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000} lortzeko, \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000} balioari kendu \frac{83344647990241}{12800000000}.

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

-6 lortzeko, biderkatu -1 eta 6.

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

Kendu B\times 6 bi aldeetatik.

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

Modu arruntean dago ekuazioa.

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

Zatitu ekuazioaren bi aldeak -6 balioarekin.

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

-6 balioarekin zatituz gero, -6 balioarekiko biderketa desegiten da.

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

Zatitu \frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}-6B balioa -6 balioarekin.

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

Ebatzi: B

$$B=A+10275.7573661003795573605550886065096894916352618741902033984661102294921875$$

Ekuazio lineala ebazteko urratsak

Murriztu \frac{46}{100} zatikia gai txikienera, 2 bakanduta eta ezeztatuta.

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

Adierazi \frac{\frac{23}{50}}{4} frakzio bakar gisa.

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

200 lortzeko, biderkatu 50 eta 4.

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

\frac{223}{200} lortzeko, gehitu 1 eta \frac{23}{200}.

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

\frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000} lortzeko, egin \frac{223}{200} ber 24.

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

\frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000} lortzeko, biderkatu 5000 eta \frac{228726620476342311322986907121740662480032913978015824641}{16777216000000000000000000000000000000000000000000000000}.

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

Hedatu \frac{4.5}{100} zenbakitzailea eta izendatzailea 10 balioarekin biderkatuta.

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

Murriztu \frac{45}{1000} zatikia gai txikienera, 5 bakanduta eta ezeztatuta.

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

\frac{209}{200} lortzeko, gehitu 1 eta \frac{9}{200}.

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

\frac{83344647990241}{64000000000000} lortzeko, egin \frac{209}{200} ber 6.

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

\frac{83344647990241}{12800000000} lortzeko, biderkatu 5000 eta \frac{83344647990241}{64000000000000}.

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

\frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000} lortzeko, \frac{228726620476342311322986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000} balioari kendu \frac{83344647990241}{12800000000}.

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

Gehitu A\times 6 bi aldeetan.

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

Modu arruntean dago ekuazioa.

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

Zatitu ekuazioaren bi aldeak 6 balioarekin.

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

6 balioarekin zatituz gero, 6 balioarekiko biderketa desegiten da.

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

Zatitu \frac{206878321073588574618986907121740662480032913978015824641}{3355443200000000000000000000000000000000000000000000}+6A balioa 6 balioarekin.

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