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

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

Datrys ar gyfer σ_x

$$\sigma _{x}=\sqrt{2}\approx 1.414213562$$

$$\sigma _{x}=-\sqrt{2}\approx -1.414213562$$

Camau drwy Ganfod Isradd

Tynnu 0 o -2 i gael -2.

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

Cyfrifo -2 i bŵer 2 a chael 4.

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

Lluosi 4 a \frac{4}{9} i gael \frac{16}{9}.

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

Lluosi 0 a 0 i gael 0.

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

Cyfrifo 0 i bŵer 2 a chael 0.

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

Lleihau'r ffracsiwn \frac{3}{9} i'r graddau lleiaf posib drwy dynnu a chanslo allan 3.

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

Lluosi 0 a \frac{1}{3} i gael 0.

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

Adio \frac{16}{9} a 0 i gael \frac{16}{9}.

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

Lluosi 1 a 0 i gael 0.

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

Cyfrifo 0 i bŵer 2 a chael 0.

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

Adio \frac{16}{9} a 0 i gael \frac{16}{9}.

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

Adio \frac{16}{9} a \frac{2}{9} i gael 2.

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

Cymryd isradd dwy ochr yr hafaliad.

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

Camau gan Ddefnyddio’r Fformiwla Cwadratig

Tynnu 0 o -2 i gael -2.

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

Cyfrifo -2 i bŵer 2 a chael 4.

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

Lluosi 4 a \frac{4}{9} i gael \frac{16}{9}.

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

Lluosi 0 a 0 i gael 0.

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

Cyfrifo 0 i bŵer 2 a chael 0.

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

Lleihau'r ffracsiwn \frac{3}{9} i'r graddau lleiaf posib drwy dynnu a chanslo allan 3.

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

Lluosi 0 a \frac{1}{3} i gael 0.

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

Adio \frac{16}{9} a 0 i gael \frac{16}{9}.

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

Lluosi 1 a 0 i gael 0.

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

Cyfrifo 0 i bŵer 2 a chael 0.

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

Adio \frac{16}{9} a 0 i gael \frac{16}{9}.

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

Adio \frac{16}{9} a \frac{2}{9} i gael 2.

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

Tynnu 2 o'r ddwy ochr.

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

Mae’r hafaliad hwn yn y ffurf safonol: ax^{2}+bx+c=0. Amnewidiwch 1 am a, 0 am b, a -2 am c yn y fformiwla gwadratig, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Sgwâr 0.

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

Lluoswch -4 â -2.

$$\sigma _{x}=\frac{0±\sqrt{8}}{2}$$

Cymryd isradd 8.

$$\sigma _{x}=\frac{0±2\sqrt{2}}{2}$$

Datryswch yr hafaliad \sigma _{x}=\frac{0±2\sqrt{2}}{2} pan fydd ± yn plws.

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

Datryswch yr hafaliad \sigma _{x}=\frac{0±2\sqrt{2}}{2} pan fydd ± yn minws.

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

Mae’r hafaliad wedi’i ddatrys nawr.

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