Whakaoti i te (4k)^2-4(6)(k^2-1)=0

$$( 4 k ) ^ { 2 } - 4 ( 6 ) ( k ^ { 2 } - 1 ) = 0$$

Whakaoti mō k

$$k=\sqrt{3}\approx 1.732050808$$

$$k=-\sqrt{3}\approx -1.732050808$$

Ngā Upane mā te Kimi Pūtakerua

Whakarohaina te \left(4k\right)^{2}.

$$4^{2}k^{2}-4\times 6\left(k^{2}-1\right)=0$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16k^{2}-4\times 6\left(k^{2}-1\right)=0$$

Whakareatia te 4 ki te 6, ka 24.

$$16k^{2}-24\left(k^{2}-1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -24 ki te k^{2}-1.

$$16k^{2}-24k^{2}+24=0$$

Pahekotia te 16k^{2} me -24k^{2}, ka -8k^{2}.

$$-8k^{2}+24=0$$

Tangohia te 24 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-8k^{2}=-24$$

Whakawehea ngā taha e rua ki te -8.

$$k^{2}=\frac{-24}{-8}$$

Whakawehea te -24 ki te -8, kia riro ko 3.

$$k^{2}=3$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$k=\sqrt{3} k=-\sqrt{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakarohaina te \left(4k\right)^{2}.

$$4^{2}k^{2}-4\times 6\left(k^{2}-1\right)=0$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16k^{2}-4\times 6\left(k^{2}-1\right)=0$$

Whakareatia te 4 ki te 6, ka 24.

$$16k^{2}-24\left(k^{2}-1\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -24 ki te k^{2}-1.

$$16k^{2}-24k^{2}+24=0$$

Pahekotia te 16k^{2} me -24k^{2}, ka -8k^{2}.

$$-8k^{2}+24=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -8 mō a, 0 mō b, me 24 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\left(-8\right)\times 24}}{2\left(-8\right)}$$

Pūrua 0.

$$k=\frac{0±\sqrt{-4\left(-8\right)\times 24}}{2\left(-8\right)}$$

Whakareatia -4 ki te -8.

$$k=\frac{0±\sqrt{32\times 24}}{2\left(-8\right)}$$

Whakareatia 32 ki te 24.

$$k=\frac{0±\sqrt{768}}{2\left(-8\right)}$$

Tuhia te pūtakerua o te 768.

$$k=\frac{0±16\sqrt{3}}{2\left(-8\right)}$$

Whakareatia 2 ki te -8.

$$k=\frac{0±16\sqrt{3}}{-16}$$

Nā, me whakaoti te whārite k=\frac{0±16\sqrt{3}}{-16} ina he tāpiri te ±.

$$k=-\sqrt{3}$$

Nā, me whakaoti te whārite k=\frac{0±16\sqrt{3}}{-16} ina he tango te ±.

$$k=\sqrt{3}$$

Kua oti te whārite te whakatau.

$$k=-\sqrt{3} k=\sqrt{3}$$