Whakaoti i te (a-R)^2+3a^2=R^2

$$( a - R ) ^ { 2 } + 3 a ^ { 2 } = R ^ { 2 }$$

Whakaoti mō R (complex solution)

$$\left\{\begin{matrix}\\R=2a\text{, }&\text{unconditionally}\\R\in \mathrm{C}\text{, }&a=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(p-q\right)^{2}=p^{2}-2pq+q^{2} hei whakaroha \left(a-R\right)^{2}.

$$a^{2}-2aR+R^{2}+3a^{2}=R^{2}$$

Pahekotia te a^{2} me 3a^{2}, ka 4a^{2}.

$$4a^{2}-2aR+R^{2}=R^{2}$$

Tangohia te R^{2} mai i ngā taha e rua.

$$4a^{2}-2aR+R^{2}-R^{2}=0$$

Pahekotia te R^{2} me -R^{2}, ka 0.

$$4a^{2}-2aR=0$$

Tangohia te 4a^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-2aR=-4a^{2}$$

He hanga arowhānui tō te whārite.

$$\left(-2a\right)R=-4a^{2}$$

Whakawehea ngā taha e rua ki te -2a.

$$\frac{\left(-2a\right)R}{-2a}=-\frac{4a^{2}}{-2a}$$

Mā te whakawehe ki te -2a ka wetekia te whakareanga ki te -2a.

$$R=-\frac{4a^{2}}{-2a}$$

Whakawehe -4a^{2} ki te -2a.

$$R=2a$$

Whakaoti mō R

$$\left\{\begin{matrix}\\R=2a\text{, }&\text{unconditionally}\\R\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(p-q\right)^{2}=p^{2}-2pq+q^{2} hei whakaroha \left(a-R\right)^{2}.

$$a^{2}-2aR+R^{2}+3a^{2}=R^{2}$$

Pahekotia te a^{2} me 3a^{2}, ka 4a^{2}.

$$4a^{2}-2aR+R^{2}=R^{2}$$

Tangohia te R^{2} mai i ngā taha e rua.

$$4a^{2}-2aR+R^{2}-R^{2}=0$$

Pahekotia te R^{2} me -R^{2}, ka 0.

$$4a^{2}-2aR=0$$

Tangohia te 4a^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-2aR=-4a^{2}$$

He hanga arowhānui tō te whārite.

$$\left(-2a\right)R=-4a^{2}$$

Whakawehea ngā taha e rua ki te -2a.

$$\frac{\left(-2a\right)R}{-2a}=-\frac{4a^{2}}{-2a}$$

Mā te whakawehe ki te -2a ka wetekia te whakareanga ki te -2a.

$$R=-\frac{4a^{2}}{-2a}$$

Whakawehe -4a^{2} ki te -2a.

$$R=2a$$

Whakaoti mō a

$$a=\frac{R}{2}$$

$$a=0$$