x^2-3x/3x^2+16x-2=0 eching

$$\frac{ { x }^{ 2 } -3x }{ 3 { x }^{ 2 } +16x-2 } =0$$

x uchun yechish

$$x=3$$

$$x=0$$

Faktorlash qadamlari

Tenglamaning ikkala tarafini 3\left(x-\left(-\frac{1}{3}\sqrt{70}-\frac{8}{3}\right)\right)\left(x-\left(\frac{1}{3}\sqrt{70}-\frac{8}{3}\right)\right) ga ko'paytirish.

$$x^{2}-3x=0$$

x omili.

$$x\left(x-3\right)=0$$

Tenglamani yechish uchun x=0 va x-3=0 ni yeching.

$$x=0 x=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 3\left(x-\left(-\frac{1}{3}\sqrt{70}-\frac{8}{3}\right)\right)\left(x-\left(\frac{1}{3}\sqrt{70}-\frac{8}{3}\right)\right) ga ko'paytirish.

$$x^{2}-3x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -3 ni b va 0 ni c bilan almashtiring.

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

\left(-3\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±3}{2}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±3}{2}$$

x=\frac{3±3}{2} tenglamasini yeching, bunda ± musbat. 3 ni 3 ga qo'shish.

$$x=\frac{6}{2}$$

6 ni 2 ga bo'lish.

$$x=3$$

x=\frac{3±3}{2} tenglamasini yeching, bunda ± manfiy. 3 dan 3 ni ayirish.

$$x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=3 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 3\left(x-\left(-\frac{1}{3}\sqrt{70}-\frac{8}{3}\right)\right)\left(x-\left(\frac{1}{3}\sqrt{70}-\frac{8}{3}\right)\right) ga ko'paytirish.

$$x^{2}-3x=0$$

-3 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{2} olish uchun. Keyin, -\frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$x^{2}-3x+\frac{9}{4}=\frac{9}{4}$$

x^{2}-3x+\frac{9}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Qisqartirish.

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

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=3 x=0$$