frac{sqrt{6}}{sqrt{2}tsqrt{3}}=frac{sqrt{6}(sqrt{2}-sqrt{3})}{(sqrt{2}+sqrt{3})(sqrt{2}-sqrt{3})}= eching

$$\frac { \sqrt { 6 } } { \sqrt { 2 } t \sqrt { 3 } } = \frac { \sqrt { 6 } ( \sqrt { 2 } - \sqrt { 3 } ) } { ( \sqrt { 2 } + \sqrt { 3 } ) ( \sqrt { 2 } - \sqrt { 3 } ) } =$$

t uchun yechish

$$t = \frac{2 \sqrt{3} + 3 \sqrt{2}}{6} \approx 1,28445705$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\sqrt{2} va \sqrt{3} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\sqrt{6}}{\sqrt{6}t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}$$

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

$$\frac{\sqrt{6}\sqrt{6}}{\left(\sqrt{6}\right)^{2}t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}$$

\sqrt{6} kvadrati – 6.

$$\frac{\sqrt{6}\sqrt{6}}{6t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}$$

6 hosil qilish uchun \sqrt{6} va \sqrt{6} ni ko'paytirish.

$$\frac{6}{6t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}$$

Hisoblang: \left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{6}{6t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}\right)^{2}-\left(\sqrt{3}\right)^{2}}$$

\sqrt{2} kvadratini chiqarish. \sqrt{3} kvadratini chiqarish.

$$\frac{6}{6t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{2-3}$$

-1 olish uchun 2 dan 3 ni ayirish.

$$\frac{6}{6t}=\frac{\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{-1}$$

Istalgan sonni -1 ga boʻlsangiz, uning qarama-qarshisi chiqadi.

$$\frac{6}{6t}=-\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)$$

\sqrt{6} ga \sqrt{2}-\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{6}{6t}=-\left(\sqrt{6}\sqrt{2}-\sqrt{6}\sqrt{3}\right)$$

Faktor: 6=2\times 3. \sqrt{2\times 3} koʻpaytmasining kvadrat ildizini \sqrt{2}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{6}{6t}=-\left(\sqrt{2}\sqrt{3}\sqrt{2}-\sqrt{6}\sqrt{3}\right)$$

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

$$\frac{6}{6t}=-\left(2\sqrt{3}-\sqrt{6}\sqrt{3}\right)$$

Faktor: 6=3\times 2. \sqrt{3\times 2} koʻpaytmasining kvadrat ildizini \sqrt{3}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{6}{6t}=-\left(2\sqrt{3}-\sqrt{3}\sqrt{2}\sqrt{3}\right)$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$\frac{6}{6t}=-\left(2\sqrt{3}-3\sqrt{2}\right)$$

2\sqrt{3}-3\sqrt{2} teskarisini topish uchun har birining teskarisini toping.

$$\frac{6}{6t}=-2\sqrt{3}+3\sqrt{2}$$

t qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 6t ga ko'paytirish.

$$6=-2\sqrt{3}\times 6t+3\sqrt{2}\times 6t$$

Shartlarni qayta saralash.

$$6=3\times 6\sqrt{2}t-2\times 6\sqrt{3}t$$

Ko‘paytirishlarni bajaring.

$$6=18\sqrt{2}t-12\sqrt{3}t$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$18\sqrt{2}t-12\sqrt{3}t=6$$

t'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(18\sqrt{2}-12\sqrt{3}\right)t=6$$

Ikki tarafini 18\sqrt{2}-12\sqrt{3} ga bo‘ling.

$$\frac{\left(18\sqrt{2}-12\sqrt{3}\right)t}{18\sqrt{2}-12\sqrt{3}}=\frac{6}{18\sqrt{2}-12\sqrt{3}}$$

18\sqrt{2}-12\sqrt{3} ga bo'lish 18\sqrt{2}-12\sqrt{3} ga ko'paytirishni bekor qiladi.

$$t=\frac{6}{18\sqrt{2}-12\sqrt{3}}$$

6 ni 18\sqrt{2}-12\sqrt{3} ga bo'lish.

$$t=\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{3}$$