Whakaoti i te ax^2+b^2-2ab^2=(b-ab)x

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

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}a=\frac{b}{x+2b}\text{, }&x\neq -2b\\a\in \mathrm{C}\text{, }&b=x\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te b-ab ki te x.

$$ax^{2}+b^{2}-2ab^{2}=bx-abx$$

Me tāpiri te abx ki ngā taha e rua.

$$ax^{2}+b^{2}-2ab^{2}+abx=bx$$

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

$$ax^{2}-2ab^{2}+abx=bx-b^{2}$$

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

$$\left(x^{2}-2b^{2}+bx\right)a=bx-b^{2}$$

He hanga arowhānui tō te whārite.

$$\left(x^{2}+bx-2b^{2}\right)a=bx-b^{2}$$

Whakawehea ngā taha e rua ki te x^{2}-2b^{2}+bx.

$$\frac{\left(x^{2}+bx-2b^{2}\right)a}{x^{2}+bx-2b^{2}}=\frac{b\left(x-b\right)}{x^{2}+bx-2b^{2}}$$

Mā te whakawehe ki te x^{2}-2b^{2}+bx ka wetekia te whakareanga ki te x^{2}-2b^{2}+bx.

$$a=\frac{b\left(x-b\right)}{x^{2}+bx-2b^{2}}$$

Whakawehe b\left(x-b\right) ki te x^{2}-2b^{2}+bx.

$$a=\frac{b}{x+2b}$$

Whakaoti mō a

$$\left\{\begin{matrix}a=\frac{b}{x+2b}\text{, }&x\neq -2b\\a\in \mathrm{R}\text{, }&x=b\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te b-ab ki te x.

$$ax^{2}+b^{2}-2ab^{2}=bx-abx$$

Me tāpiri te abx ki ngā taha e rua.

$$ax^{2}+b^{2}-2ab^{2}+abx=bx$$

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

$$ax^{2}-2ab^{2}+abx=bx-b^{2}$$

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

$$\left(x^{2}-2b^{2}+bx\right)a=bx-b^{2}$$

He hanga arowhānui tō te whārite.

$$\left(x^{2}+bx-2b^{2}\right)a=bx-b^{2}$$

Whakawehea ngā taha e rua ki te x^{2}-2b^{2}+bx.

$$\frac{\left(x^{2}+bx-2b^{2}\right)a}{x^{2}+bx-2b^{2}}=\frac{b\left(x-b\right)}{x^{2}+bx-2b^{2}}$$

Mā te whakawehe ki te x^{2}-2b^{2}+bx ka wetekia te whakareanga ki te x^{2}-2b^{2}+bx.

$$a=\frac{b\left(x-b\right)}{x^{2}+bx-2b^{2}}$$

Whakawehe b\left(x-b\right) ki te x^{2}-2b^{2}+bx.

$$a=\frac{b}{x+2b}$$

Whakaoti mō b (complex solution)

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

Whakaoti mō b

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