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

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

x uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{44633466}{5134334344334} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

\sqrt{\frac{58}{99999}} boʻlinmasining kvadrat ildizini \frac{\sqrt{58}}{\sqrt{99999}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

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

Faktor: 99999=3^{2}\times 11111. \sqrt{3^{2}\times 11111} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{11111} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

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

\frac{\sqrt{58}}{3\sqrt{11111}} maxrajini \sqrt{11111} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{11111} kvadrati – 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} va \sqrt{11111} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

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

33333 hosil qilish uchun 3 va 11111 ni ko'paytirish.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{22316733}{2567167172167} ni \frac{\sqrt{644438}}{33333} ga ko‘paytiring.

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

Surat va maxrajdagi ikkala 3 ni qisqartiring.

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

\frac{5}{8} ni \frac{5}{9} ga bo'lish \frac{5}{8} ga k'paytirish \frac{5}{9} ga qaytarish.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{8} ni \frac{9}{5} ga ko‘paytiring.

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

Surat va maxrajdagi ikkala 5 ni qisqartiring.

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

\sqrt{\frac{9}{8}} boʻlinmasining kvadrat ildizini \frac{\sqrt{9}}{\sqrt{8}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

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

9 ning kvadrat ildizini hisoblab, 3 natijaga ega bo‘ling.

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

Faktor: 8=2^{2}\times 2. \sqrt{2^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

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

\frac{3}{2\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{2} kvadrati – 2.

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

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

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

663434\times \frac{3\sqrt{2}}{4} ni yagona kasrga aylantiring.

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

\frac{663434\times 3\sqrt{2}}{4}x ni yagona kasrga aylantiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 11111\times 2567167172167 va 4 ning eng kichik umumiy karralisi 114095177799790148. \frac{7438911\sqrt{644438}}{11111\times 2567167172167} ni \frac{4}{4} marotabaga ko'paytirish. \frac{663434\times 3\sqrt{2}x}{4} ni \frac{28523794449947537}{28523794449947537} marotabaga ko'paytirish.

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

\frac{4\times 7438911\sqrt{644438}}{114095177799790148} va \frac{28523794449947537\times 663434\times 3\sqrt{2}x}{114095177799790148} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

4\times 7438911\sqrt{644438}+28523794449947537\times 663434\times 3\sqrt{2}x ichidagi ko‘paytirishlarni bajaring.

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

Ikkala tarafini 114095177799790148 ga ko‘paytiring.

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

1026856600198111332 hosil qilish uchun 9 va 114095177799790148 ni ko'paytirish.

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

Ikkala tarafdan 29755644\sqrt{644438} ni ayirish.

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

Ikki tarafini 56770965141319482786174\sqrt{2} ga bo‘ling.

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

56770965141319482786174\sqrt{2} ga bo'lish 56770965141319482786174\sqrt{2} ga ko'paytirishni bekor qiladi.

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

1026856600198111332-29755644\sqrt{644438} ni 56770965141319482786174\sqrt{2} ga bo'lish.

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