Whakaoti i te a+b^2=(a-b)^2

$$a + b ^ { 2 } = ( a - b ) ^ { 2 }$$

Whakaoti mō b (complex solution)

$$\left\{\begin{matrix}\\b=\frac{a-1}{2}\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&a=0\end{matrix}\right.$$

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-b\right)^{2}.

$$a+b^{2}=a^{2}-2ab+b^{2}$$

Me tāpiri te 2ab ki ngā taha e rua.

$$a+b^{2}+2ab=a^{2}+b^{2}$$

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

$$a+b^{2}+2ab-b^{2}=a^{2}$$

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

$$a+2ab=a^{2}$$

Tangohia te a mai i ngā taha e rua.

$$2ab=a^{2}-a$$

Whakawehea ngā taha e rua ki te 2a.

$$\frac{2ab}{2a}=\frac{a\left(a-1\right)}{2a}$$

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

$$b=\frac{a\left(a-1\right)}{2a}$$

Whakawehe a\left(-1+a\right) ki te 2a.

$$b=\frac{a-1}{2}$$

Whakaoti mō b

$$\left\{\begin{matrix}\\b=\frac{a-1}{2}\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$

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-b\right)^{2}.

$$a+b^{2}=a^{2}-2ab+b^{2}$$

Me tāpiri te 2ab ki ngā taha e rua.

$$a+b^{2}+2ab=a^{2}+b^{2}$$

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

$$a+b^{2}+2ab-b^{2}=a^{2}$$

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

$$a+2ab=a^{2}$$

Tangohia te a mai i ngā taha e rua.

$$2ab=a^{2}-a$$

Whakawehea ngā taha e rua ki te 2a.

$$\frac{2ab}{2a}=\frac{a\left(a-1\right)}{2a}$$

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

$$b=\frac{a\left(a-1\right)}{2a}$$

Whakawehe a\left(-1+a\right) ki te 2a.

$$b=\frac{a-1}{2}$$

Whakaoti mō a

$$a=2b+1$$

$$a=0$$