Lahenda 44633466/5134334344334*sqrt{58/99999}+663434sqrt{5/8/frac{5{9}}}x=9

$$\frac{ 44633466 }{ 5134334344334 } \times \sqrt{ \frac{ 58 }{ 99999 } } +663434 \sqrt{ \frac{ \frac{ 5 }{ 8 } }{ \frac{ 5 }{ 9 } } } x=9$$

Lahendage ja leidke x

$$x=\frac{3\sqrt{2}}{331717}-\frac{4959274\sqrt{322219}}{9461827523553247131029}\approx 0,00001279$$

Juhised lineaarvõrrandi lahendamiseks

Taandage murd \frac{44633466}{5134334344334} vähimale ühiskordsele, eraldades ja taandades arvu 2.

$$\frac{22316733}{2567167172167}\sqrt{\frac{58}{99999}}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Kirjutage: allüksus \sqrt{\frac{58}{99999}}: allüksus juured \frac{\sqrt{58}}{\sqrt{99999}}.

$$\frac{22316733}{2567167172167}\times \frac{\sqrt{58}}{\sqrt{99999}}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Tegurda 99999=3^{2}\times 11111. Kirjutage \sqrt{3^{2}\times 11111} toote juured, kui see ruut \sqrt{3^{2}}\sqrt{11111}. Leidke 3^{2} ruutjuur.

$$\frac{22316733}{2567167172167}\times \frac{\sqrt{58}}{3\sqrt{11111}}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Ratsionaliseerige korrutades lugeja ja \sqrt{11111} nimetaja \frac{\sqrt{58}}{3\sqrt{11111}} nimetaja.

$$\frac{22316733}{2567167172167}\times \frac{\sqrt{58}\sqrt{11111}}{3\left(\sqrt{11111}\right)^{2}}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

\sqrt{11111} ruut on 11111.

$$\frac{22316733}{2567167172167}\times \frac{\sqrt{58}\sqrt{11111}}{3\times 11111}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

\sqrt{58} ja \sqrt{11111} korrutage numbrid, mis on sama juur.

$$\frac{22316733}{2567167172167}\times \frac{\sqrt{644438}}{3\times 11111}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Korrutage 3 ja 11111, et leida 33333.

$$\frac{22316733}{2567167172167}\times \frac{\sqrt{644438}}{33333}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Korrutage omavahel \frac{22316733}{2567167172167} ja \frac{\sqrt{644438}}{33333}. Seejärel taandage murd võimaluse korral vähimale ühiskordsele.

$$\frac{22316733\sqrt{644438}}{2567167172167\times 33333}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Taandage 3 nii lugejas kui ka nimetajas.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Jagage \frac{5}{8} väärtusega \frac{5}{9}, korrutades \frac{5}{8} väärtuse \frac{5}{9} pöördväärtusega.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\sqrt{\frac{5}{8}\times \frac{9}{5}}x=9$$

Korrutage omavahel \frac{5}{8} ja \frac{9}{5}. Seejärel taandage murd võimaluse korral vähimale ühiskordsele.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\sqrt{\frac{5\times 9}{8\times 5}}x=9$$

Taandage 5 nii lugejas kui ka nimetajas.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\sqrt{\frac{9}{8}}x=9$$

Kirjutage: allüksus \sqrt{\frac{9}{8}}: allüksus juured \frac{\sqrt{9}}{\sqrt{8}}.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\times \frac{\sqrt{9}}{\sqrt{8}}x=9$$

Arvutage 9 ruutjuur, et saada 3.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\times \frac{3}{\sqrt{8}}x=9$$

Tegurda 8=2^{2}\times 2. Kirjutage \sqrt{2^{2}\times 2} toote juured, kui see ruut \sqrt{2^{2}}\sqrt{2}. Leidke 2^{2} ruutjuur.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\times \frac{3}{2\sqrt{2}}x=9$$

Ratsionaliseerige korrutades lugeja ja \sqrt{2} nimetaja \frac{3}{2\sqrt{2}} nimetaja.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\times \frac{3\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}x=9$$

\sqrt{2} ruut on 2.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\times \frac{3\sqrt{2}}{2\times 2}x=9$$

Korrutage 2 ja 2, et leida 4.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\times \frac{3\sqrt{2}}{4}x=9$$

Avaldage 663434\times \frac{3\sqrt{2}}{4} ühe murdarvuna.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+\frac{663434\times 3\sqrt{2}}{4}x=9$$

Avaldage \frac{663434\times 3\sqrt{2}}{4}x ühe murdarvuna.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+\frac{663434\times 3\sqrt{2}x}{4}=9$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. 11111\times 2567167172167 ja 4 vähim ühiskordne on 114095177799790148. Korrutage omavahel \frac{7438911\sqrt{644438}}{11111\times 2567167172167} ja \frac{4}{4}. Korrutage omavahel \frac{663434\times 3\sqrt{2}x}{4} ja \frac{28523794449947537}{28523794449947537}.

$$\frac{4\times 7438911\sqrt{644438}}{114095177799790148}+\frac{28523794449947537\times 663434\times 3\sqrt{2}x}{114095177799790148}=9$$

Kuna murdudel \frac{4\times 7438911\sqrt{644438}}{114095177799790148} ja \frac{28523794449947537\times 663434\times 3\sqrt{2}x}{114095177799790148} on sama nimetaja, liitke nende lugejad.

$$\frac{4\times 7438911\sqrt{644438}+28523794449947537\times 663434\times 3\sqrt{2}x}{114095177799790148}=9$$

Tehke korrutustehted võrrandis 4\times 7438911\sqrt{644438}+28523794449947537\times 663434\times 3\sqrt{2}x.

$$\frac{29755644\sqrt{644438}+56770965141319482786174\sqrt{2}x}{114095177799790148}=9$$

Korrutage mõlemad pooled 114095177799790148-ga.

$$29755644\sqrt{644438}+56770965141319482786174\sqrt{2}x=9\times 114095177799790148$$

Korrutage 9 ja 114095177799790148, et leida 1026856600198111332.

$$29755644\sqrt{644438}+56770965141319482786174\sqrt{2}x=1026856600198111332$$

Lahutage mõlemast poolest 29755644\sqrt{644438}.

$$56770965141319482786174\sqrt{2}x=1026856600198111332-29755644\sqrt{644438}$$

Jagage mõlemad pooled 56770965141319482786174\sqrt{2}-ga.

$$\frac{56770965141319482786174\sqrt{2}x}{56770965141319482786174\sqrt{2}}=\frac{1026856600198111332-29755644\sqrt{644438}}{56770965141319482786174\sqrt{2}}$$

56770965141319482786174\sqrt{2}-ga jagamine võtab 56770965141319482786174\sqrt{2}-ga korrutamise tagasi.

$$x=\frac{1026856600198111332-29755644\sqrt{644438}}{56770965141319482786174\sqrt{2}}$$

Jagage 1026856600198111332-29755644\sqrt{644438} väärtusega 56770965141319482786174\sqrt{2}.

$$x=\frac{3\sqrt{2}}{331717}-\frac{4959274\sqrt{322219}}{9461827523553247131029}$$