3x/3+sqrt{3}-frac{2xsqrt{3}}{3-1}=27/2sqrt{3} eching

$$\frac{ 3x }{ 3+ \sqrt{ 3 } } - \frac{ 2x \sqrt{ 3 } }{ 3-1 } = \frac{ 27 }{ 2 \sqrt{ 3 } }$$

x uchun yechish

$$x=\frac{-3\sqrt{3}-9}{2}\approx -7,098076211$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{3x}{3+\sqrt{3}} maxrajini 3-\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{3x\left(3-\sqrt{3}\right)}{\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)}-\frac{2x\sqrt{3}}{3-1}=\frac{27}{2\sqrt{3}}$$

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

$$\frac{3x\left(3-\sqrt{3}\right)}{3^{2}-\left(\sqrt{3}\right)^{2}}-\frac{2x\sqrt{3}}{3-1}=\frac{27}{2\sqrt{3}}$$

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

$$\frac{3x\left(3-\sqrt{3}\right)}{9-3}-\frac{2x\sqrt{3}}{3-1}=\frac{27}{2\sqrt{3}}$$

6 olish uchun 9 dan 3 ni ayirish.

$$\frac{3x\left(3-\sqrt{3}\right)}{6}-\frac{2x\sqrt{3}}{3-1}=\frac{27}{2\sqrt{3}}$$

2 olish uchun 3 dan 1 ni ayirish.

$$\frac{3x\left(3-\sqrt{3}\right)}{6}-\frac{2x\sqrt{3}}{2}=\frac{27}{2\sqrt{3}}$$

2 va 2 ni qisqartiring.

$$\frac{3x\left(3-\sqrt{3}\right)}{6}-x\sqrt{3}=\frac{27}{2\sqrt{3}}$$

\frac{27}{2\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{3x\left(3-\sqrt{3}\right)}{6}-x\sqrt{3}=\frac{27\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{3x\left(3-\sqrt{3}\right)}{6}-x\sqrt{3}=\frac{27\sqrt{3}}{2\times 3}$$

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{3x\left(3-\sqrt{3}\right)}{6}-x\sqrt{3}=\frac{9\sqrt{3}}{2}$$

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

$$\frac{9x-3\sqrt{3}x}{6}-x\sqrt{3}=\frac{9\sqrt{3}}{2}$$

Tenglamaning ikkala tarafini 6 ga, 6,2 ning eng kichik karralisiga ko‘paytiring.

$$9x-3\sqrt{3}x-6x\sqrt{3}=3\times 9\sqrt{3}$$

Shartlarni qayta saralash.

$$-6\sqrt{3}x-3\sqrt{3}x+9x=3\times 9\sqrt{3}$$

-9\sqrt{3}x ni olish uchun -6\sqrt{3}x va -3\sqrt{3}x ni birlashtirish.

$$-9\sqrt{3}x+9x=3\times 9\sqrt{3}$$

27 hosil qilish uchun 3 va 9 ni ko'paytirish.

$$-9\sqrt{3}x+9x=27\sqrt{3}$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-9\sqrt{3}+9\right)x=27\sqrt{3}$$

Tenglama standart shaklda.

$$\left(9-9\sqrt{3}\right)x=27\sqrt{3}$$

Ikki tarafini -9\sqrt{3}+9 ga bo‘ling.

$$\frac{\left(9-9\sqrt{3}\right)x}{9-9\sqrt{3}}=\frac{27\sqrt{3}}{9-9\sqrt{3}}$$

-9\sqrt{3}+9 ga bo'lish -9\sqrt{3}+9 ga ko'paytirishni bekor qiladi.

$$x=\frac{27\sqrt{3}}{9-9\sqrt{3}}$$

27\sqrt{3} ni -9\sqrt{3}+9 ga bo'lish.

$$x=\frac{-3\sqrt{3}-9}{2}$$