Whakaoti i te 4x^2-3kx+1=0

$$4 x ^ { 2 } - 3 k x + 1 = 0$$

Whakaoti mō k

$$k=\frac{4x}{3}+\frac{1}{3x}$$

$$x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$-3kx+1=-4x^{2}$$

Tangohia te 1 mai i ngā taha e rua.

$$-3kx=-4x^{2}-1$$

He hanga arowhānui tō te whārite.

$$\left(-3x\right)k=-4x^{2}-1$$

Whakawehea ngā taha e rua ki te -3x.

$$\frac{\left(-3x\right)k}{-3x}=\frac{-4x^{2}-1}{-3x}$$

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

$$k=\frac{-4x^{2}-1}{-3x}$$

Whakawehe -4x^{2}-1 ki te -3x.

$$k=\frac{4x}{3}+\frac{1}{3x}$$

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{9k^{2}-16}+3k}{8}$$

$$x=\frac{-\sqrt{9k^{2}-16}+3k}{8}$$

Whakaoti mō x

$$x=\frac{\sqrt{9k^{2}-16}+3k}{8}$$

$$x=\frac{-\sqrt{9k^{2}-16}+3k}{8}\text{, }|k|\geq \frac{4}{3}$$