frac{sqrt{2}}{frac{sqrt{5}}{3}}=x/sqrt{5/sqrt{6}} eching

$$\frac { \sqrt { 2 } } { \frac { \sqrt { 5 } } { 3 } } = \frac { x } { \frac { \sqrt { 5 } } { \sqrt { 6 } } }$$

x uchun yechish

$$x=\sqrt{3}\approx 1,732050808$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\sqrt{2} ni \frac{\sqrt{5}}{3} ga bo'lish \sqrt{2} ga k'paytirish \frac{\sqrt{5}}{3} ga qaytarish.

$$\frac{\sqrt{2}\times 3}{\sqrt{5}}=\frac{x}{\frac{\sqrt{5}}{\sqrt{6}}}$$

\frac{\sqrt{2}\times 3}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{2}\times 3\sqrt{5}}{\left(\sqrt{5}\right)^{2}}=\frac{x}{\frac{\sqrt{5}}{\sqrt{6}}}$$

\sqrt{5} kvadrati – 5.

$$\frac{\sqrt{2}\times 3\sqrt{5}}{5}=\frac{x}{\frac{\sqrt{5}}{\sqrt{6}}}$$

\sqrt{2} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\sqrt{10}\times 3}{5}=\frac{x}{\frac{\sqrt{5}}{\sqrt{6}}}$$

x ni \frac{\sqrt{5}}{\sqrt{6}} ga bo'lish x ga k'paytirish \frac{\sqrt{5}}{\sqrt{6}} ga qaytarish.

$$\frac{\sqrt{10}\times 3}{5}=\frac{x\sqrt{6}}{\sqrt{5}}$$

\frac{x\sqrt{6}}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{10}\times 3}{5}=\frac{x\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{\sqrt{10}\times 3}{5}=\frac{x\sqrt{6}\sqrt{5}}{5}$$

\sqrt{6} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\sqrt{10}\times 3}{5}=\frac{x\sqrt{30}}{5}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{x\sqrt{30}}{5}=\frac{\sqrt{10}\times 3}{5}$$

Tenglamaning ikkala tarafini 5 ga ko'paytirish.

$$x\sqrt{30}=\sqrt{10}\times 3$$

Tenglama standart shaklda.

$$\sqrt{30}x=3\sqrt{10}$$

Ikki tarafini \sqrt{30} ga bo‘ling.

$$\frac{\sqrt{30}x}{\sqrt{30}}=\frac{3\sqrt{10}}{\sqrt{30}}$$

\sqrt{30} ga bo'lish \sqrt{30} ga ko'paytirishni bekor qiladi.

$$x=\frac{3\sqrt{10}}{\sqrt{30}}$$

3\sqrt{10} ni \sqrt{30} ga bo'lish.

$$x=\sqrt{3}$$