Whakaoti i te x^2-5xy-3b=y^2

$$x ^ { 2 } - 5 x y - 3 b = y ^ { 2 }$$

Whakaoti mō b

$$b=\frac{x^{2}-5xy-y^{2}}{3}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$-5xy-3b=y^{2}-x^{2}$$

Me tāpiri te 5xy ki ngā taha e rua.

$$-3b=y^{2}-x^{2}+5xy$$

He hanga arowhānui tō te whārite.

$$-3b=y^{2}+5xy-x^{2}$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3b}{-3}=\frac{y^{2}+5xy-x^{2}}{-3}$$

Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.

$$b=\frac{y^{2}+5xy-x^{2}}{-3}$$

Whakawehe y^{2}-x^{2}+5xy ki te -3.

$$b=\frac{x^{2}-5xy-y^{2}}{3}$$

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{29y^{2}+12b}+5y}{2}$$

$$x=\frac{-\sqrt{29y^{2}+12b}+5y}{2}$$

Whakaoti mō x

$$x=\frac{\sqrt{29y^{2}+12b}+5y}{2}$$

$$x=\frac{-\sqrt{29y^{2}+12b}+5y}{2}\text{, }b\geq -\frac{29y^{2}}{12}$$