x^2=1/3x+2 eching

$$x ^ { 2 } = \frac { 1 } { 3 } x + 2$$

x uchun yechish

$$x = \frac{\sqrt{73} + 1}{6} \approx 1,590667291$$

$$x=\frac{1-\sqrt{73}}{6}\approx -1,257333958$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan \frac{1}{3}x ni ayirish.

$$x^{2}-\frac{1}{3}x=2$$

Ikkala tarafdan 2 ni ayirish.

$$x^{2}-\frac{1}{3}x-2=0$$

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

$$x=\frac{-\left(-\frac{1}{3}\right)±\sqrt{\left(-\frac{1}{3}\right)^{2}-4\left(-2\right)}}{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{3} kvadratini chiqarish.

$$x=\frac{-\left(-\frac{1}{3}\right)±\sqrt{\frac{1}{9}-4\left(-2\right)}}{2}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-\frac{1}{3}\right)±\sqrt{\frac{1}{9}+8}}{2}$$

\frac{1}{9} ni 8 ga qo'shish.

$$x=\frac{-\left(-\frac{1}{3}\right)±\sqrt{\frac{73}{9}}}{2}$$

\frac{73}{9} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{1}{3}\right)±\frac{\sqrt{73}}{3}}{2}$$

-\frac{1}{3} ning teskarisi \frac{1}{3} ga teng.

$$x=\frac{\frac{1}{3}±\frac{\sqrt{73}}{3}}{2}$$

x=\frac{\frac{1}{3}±\frac{\sqrt{73}}{3}}{2} tenglamasini yeching, bunda ± musbat. \frac{1}{3} ni \frac{\sqrt{73}}{3} ga qo'shish.

$$x=\frac{\sqrt{73}+1}{2\times 3}$$

\frac{1+\sqrt{73}}{3} ni 2 ga bo'lish.

$$x=\frac{\sqrt{73}+1}{6}$$

x=\frac{\frac{1}{3}±\frac{\sqrt{73}}{3}}{2} tenglamasini yeching, bunda ± manfiy. \frac{1}{3} dan \frac{\sqrt{73}}{3} ni ayirish.

$$x=\frac{1-\sqrt{73}}{2\times 3}$$

\frac{1-\sqrt{73}}{3} ni 2 ga bo'lish.

$$x=\frac{1-\sqrt{73}}{6}$$

Tenglama yechildi.

$$x=\frac{\sqrt{73}+1}{6} x=\frac{1-\sqrt{73}}{6}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan \frac{1}{3}x ni ayirish.

$$x^{2}-\frac{1}{3}x=2$$

-\frac{1}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{6} olish uchun. Keyin, -\frac{1}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{6} kvadratini chiqarish.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=2+\frac{1}{36}$$

2 ni \frac{1}{36} ga qo'shish.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{73}{36}$$

x^{2}-\frac{1}{3}x+\frac{1}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{6}\right)^{2}=\frac{73}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{6}\right)^{2}}=\sqrt{\frac{73}{36}}$$

Qisqartirish.

$$x-\frac{1}{6}=\frac{\sqrt{73}}{6} x-\frac{1}{6}=-\frac{\sqrt{73}}{6}$$

\frac{1}{6} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{73}+1}{6} x=\frac{1-\sqrt{73}}{6}$$