Whakaoti i te f(x+2)-f(x-1)=26/3f(x)

$$f ( x + 2 ) - f ( x - 1 ) = \frac { 26 } { 3 } f ( x )$$

Whakaoti mō f (complex solution)

$$\left\{\begin{matrix}\\f=0\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&x=\frac{9}{26}\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te f ki te x+2.

$$fx+2f-f\left(x-1\right)=\frac{26}{3}fx$$

Whakamahia te āhuatanga tohatoha hei whakarea te f ki te x-1.

$$fx+2f-\left(fx-f\right)=\frac{26}{3}fx$$

Hei kimi i te tauaro o fx-f, kimihia te tauaro o ia taurangi.

$$fx+2f-fx+f=\frac{26}{3}fx$$

Pahekotia te fx me -fx, ka 0.

$$2f+f=\frac{26}{3}fx$$

Pahekotia te 2f me f, ka 3f.

$$3f=\frac{26}{3}fx$$

Tangohia te \frac{26}{3}fx mai i ngā taha e rua.

$$3f-\frac{26}{3}fx=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te f.

$$\left(3-\frac{26}{3}x\right)f=0$$

He hanga arowhānui tō te whārite.

$$\left(-\frac{26x}{3}+3\right)f=0$$

Whakawehe 0 ki te 3-\frac{26}{3}x.

$$f=0$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{9}{26}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&f=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te f ki te x+2.

$$fx+2f-f\left(x-1\right)=\frac{26}{3}fx$$

Whakamahia te āhuatanga tohatoha hei whakarea te f ki te x-1.

$$fx+2f-\left(fx-f\right)=\frac{26}{3}fx$$

Hei kimi i te tauaro o fx-f, kimihia te tauaro o ia taurangi.

$$fx+2f-fx+f=\frac{26}{3}fx$$

Pahekotia te fx me -fx, ka 0.

$$2f+f=\frac{26}{3}fx$$

Pahekotia te 2f me f, ka 3f.

$$3f=\frac{26}{3}fx$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{26}{3}fx=3f$$

He hanga arowhānui tō te whārite.

$$\frac{26f}{3}x=3f$$

Whakawehea ngā taha e rua ki te \frac{26}{3}f.

$$\frac{3\times \frac{26f}{3}x}{26f}=\frac{3\times 3f}{26f}$$

Mā te whakawehe ki te \frac{26}{3}f ka wetekia te whakareanga ki te \frac{26}{3}f.

$$x=\frac{3\times 3f}{26f}$$

Whakawehe 3f ki te \frac{26}{3}f.

$$x=\frac{9}{26}$$

Whakaoti mō f

$$\left\{\begin{matrix}\\f=0\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=\frac{9}{26}\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te f ki te x+2.

$$fx+2f-f\left(x-1\right)=\frac{26}{3}fx$$

Whakamahia te āhuatanga tohatoha hei whakarea te f ki te x-1.

$$fx+2f-\left(fx-f\right)=\frac{26}{3}fx$$

Hei kimi i te tauaro o fx-f, kimihia te tauaro o ia taurangi.

$$fx+2f-fx+f=\frac{26}{3}fx$$

Pahekotia te fx me -fx, ka 0.

$$2f+f=\frac{26}{3}fx$$

Pahekotia te 2f me f, ka 3f.

$$3f=\frac{26}{3}fx$$

Tangohia te \frac{26}{3}fx mai i ngā taha e rua.

$$3f-\frac{26}{3}fx=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te f.

$$\left(3-\frac{26}{3}x\right)f=0$$

He hanga arowhānui tō te whārite.

$$\left(-\frac{26x}{3}+3\right)f=0$$

Whakawehe 0 ki te 3-\frac{26}{3}x.

$$f=0$$

Whakaoti mō x

$$\left\{\begin{matrix}\\x=\frac{9}{26}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&f=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te f ki te x+2.

$$fx+2f-f\left(x-1\right)=\frac{26}{3}fx$$

Whakamahia te āhuatanga tohatoha hei whakarea te f ki te x-1.

$$fx+2f-\left(fx-f\right)=\frac{26}{3}fx$$

Hei kimi i te tauaro o fx-f, kimihia te tauaro o ia taurangi.

$$fx+2f-fx+f=\frac{26}{3}fx$$

Pahekotia te fx me -fx, ka 0.

$$2f+f=\frac{26}{3}fx$$

Pahekotia te 2f me f, ka 3f.

$$3f=\frac{26}{3}fx$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{26}{3}fx=3f$$

He hanga arowhānui tō te whārite.

$$\frac{26f}{3}x=3f$$

Whakawehea ngā taha e rua ki te \frac{26}{3}f.

$$\frac{3\times \frac{26f}{3}x}{26f}=\frac{3\times 3f}{26f}$$

Mā te whakawehe ki te \frac{26}{3}f ka wetekia te whakareanga ki te \frac{26}{3}f.

$$x=\frac{3\times 3f}{26f}$$

Whakawehe 3f ki te \frac{26}{3}f.

$$x=\frac{9}{26}$$