sqrt{3}x+sqrt{12}=x+5/sqrt{3} eching

$$\sqrt{ 3 } x+ \sqrt{ 12 } = \frac{ x+5 }{ \sqrt{ 3 } }$$

x uchun yechish

$$x=-\frac{1}{2}=-0,5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Faktor: 12=2^{2}\times 3. \sqrt{2^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

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

\frac{x+5}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{3} kvadrati – 3.

$$\sqrt{3}x+2\sqrt{3}=\frac{\left(x+5\right)\sqrt{3}}{3}$$

x+5 ga \sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Ikkala tarafdan \frac{x\sqrt{3}+5\sqrt{3}}{3} ni ayirish.

$$\sqrt{3}x+2\sqrt{3}-\frac{x\sqrt{3}+5\sqrt{3}}{3}=0$$

Ikkala tarafdan 2\sqrt{3} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$\sqrt{3}x-\frac{x\sqrt{3}+5\sqrt{3}}{3}=-2\sqrt{3}$$

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

$$3\sqrt{3}x-\left(x\sqrt{3}+5\sqrt{3}\right)=-6\sqrt{3}$$

x\sqrt{3}+5\sqrt{3} teskarisini topish uchun har birining teskarisini toping.

$$3\sqrt{3}x-x\sqrt{3}-5\sqrt{3}=-6\sqrt{3}$$

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

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

5\sqrt{3} ni ikki tarafga qo’shing.

$$2\sqrt{3}x=-6\sqrt{3}+5\sqrt{3}$$

-\sqrt{3} ni olish uchun -6\sqrt{3} va 5\sqrt{3} ni birlashtirish.

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

Ikki tarafini 2\sqrt{3} ga bo‘ling.

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

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

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

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

$$x=-\frac{1}{2}$$