sigma_x^2=(-2-0)^2*4/9+(0*0)^2*3/9+(1*0)^2+2/9= eching

$$\sigma _ { x } ^ { 2 } = ( - 2 - 0 ) ^ { 2 } \times \frac { 4 } { 9 } + ( 0 \times 0 ) ^ { 2 } \times \frac { 3 } { 9 } + ( 1 \times 0 ) ^ { 2 } + \frac { 2 } { 9 } =$$

σ_x uchun yechish

$$\sigma _{x}=\sqrt{2}\approx 1,414213562$$

$$\sigma _{x}=-\sqrt{2}\approx -1,414213562$$

Kvadrat ildizini topish bo'yicha qadamlar

-2 olish uchun -2 dan 0 ni ayirish.

$$\sigma _{x}^{2}=\left(-2\right)^{2}\times \frac{4}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

2 daraja ko‘rsatkichini -2 ga hisoblang va 4 ni qiymatni oling.

$$\sigma _{x}^{2}=4\times \frac{4}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

\frac{16}{9} hosil qilish uchun 4 va \frac{4}{9} ni ko'paytirish.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$\sigma _{x}^{2}=\frac{16}{9}+0^{2}\times \frac{3}{9}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

2 daraja ko‘rsatkichini 0 ga hisoblang va 0 ni qiymatni oling.

$$\sigma _{x}^{2}=\frac{16}{9}+0\times \frac{3}{9}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

\frac{3}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sigma _{x}^{2}=\frac{16}{9}+0\times \frac{1}{3}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

0 hosil qilish uchun 0 va \frac{1}{3} ni ko'paytirish.

$$\sigma _{x}^{2}=\frac{16}{9}+0+\left(1\times 0\right)^{2}+\frac{2}{9}$$

\frac{16}{9} olish uchun \frac{16}{9} va 0'ni qo'shing.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

0 hosil qilish uchun 1 va 0 ni ko'paytirish.

$$\sigma _{x}^{2}=\frac{16}{9}+0^{2}+\frac{2}{9}$$

2 daraja ko‘rsatkichini 0 ga hisoblang va 0 ni qiymatni oling.

$$\sigma _{x}^{2}=\frac{16}{9}+0+\frac{2}{9}$$

\frac{16}{9} olish uchun \frac{16}{9} va 0'ni qo'shing.

$$\sigma _{x}^{2}=\frac{16}{9}+\frac{2}{9}$$

2 olish uchun \frac{16}{9} va \frac{2}{9}'ni qo'shing.

$$\sigma _{x}^{2}=2$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sigma _{x}=\sqrt{2} \sigma _{x}=-\sqrt{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

-2 olish uchun -2 dan 0 ni ayirish.

$$\sigma _{x}^{2}=\left(-2\right)^{2}\times \frac{4}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

2 daraja ko‘rsatkichini -2 ga hisoblang va 4 ni qiymatni oling.

$$\sigma _{x}^{2}=4\times \frac{4}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

\frac{16}{9} hosil qilish uchun 4 va \frac{4}{9} ni ko'paytirish.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(0\times 0\right)^{2}\times \frac{3}{9}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$\sigma _{x}^{2}=\frac{16}{9}+0^{2}\times \frac{3}{9}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

2 daraja ko‘rsatkichini 0 ga hisoblang va 0 ni qiymatni oling.

$$\sigma _{x}^{2}=\frac{16}{9}+0\times \frac{3}{9}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

\frac{3}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sigma _{x}^{2}=\frac{16}{9}+0\times \frac{1}{3}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

0 hosil qilish uchun 0 va \frac{1}{3} ni ko'paytirish.

$$\sigma _{x}^{2}=\frac{16}{9}+0+\left(1\times 0\right)^{2}+\frac{2}{9}$$

\frac{16}{9} olish uchun \frac{16}{9} va 0'ni qo'shing.

$$\sigma _{x}^{2}=\frac{16}{9}+\left(1\times 0\right)^{2}+\frac{2}{9}$$

0 hosil qilish uchun 1 va 0 ni ko'paytirish.

$$\sigma _{x}^{2}=\frac{16}{9}+0^{2}+\frac{2}{9}$$

2 daraja ko‘rsatkichini 0 ga hisoblang va 0 ni qiymatni oling.

$$\sigma _{x}^{2}=\frac{16}{9}+0+\frac{2}{9}$$

\frac{16}{9} olish uchun \frac{16}{9} va 0'ni qo'shing.

$$\sigma _{x}^{2}=\frac{16}{9}+\frac{2}{9}$$

2 olish uchun \frac{16}{9} va \frac{2}{9}'ni qo'shing.

$$\sigma _{x}^{2}=2$$

Ikkala tarafdan 2 ni ayirish.

$$\sigma _{x}^{2}-2=0$$

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

$$\sigma _{x}=\frac{0±\sqrt{0^{2}-4\left(-2\right)}}{2}$$

0 kvadratini chiqarish.

$$\sigma _{x}=\frac{0±\sqrt{-4\left(-2\right)}}{2}$$

-4 ni -2 marotabaga ko'paytirish.

$$\sigma _{x}=\frac{0±\sqrt{8}}{2}$$

8 ning kvadrat ildizini chiqarish.

$$\sigma _{x}=\frac{0±2\sqrt{2}}{2}$$

\sigma _{x}=\frac{0±2\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat.

$$\sigma _{x}=\sqrt{2}$$

\sigma _{x}=\frac{0±2\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy.

$$\sigma _{x}=-\sqrt{2}$$

Tenglama yechildi.

$$\sigma _{x}=\sqrt{2} \sigma _{x}=-\sqrt{2}$$