Whakaoti i te 3/x=1/x^2quad4/2x

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

Whakaoti mō x

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x,x^{2},2x.

$$2x\times 3=2\times 1\times \frac{4}{2x}$$

Whakareatia te 2 ki te 3, ka 6.

$$6x=2\times 1\times \frac{4}{2x}$$

Whakareatia te 2 ki te 1, ka 2.

$$6x=2\times \frac{4}{2x}$$

Tuhia te 2\times \frac{4}{2x} hei hautanga kotahi.

$$6x=\frac{2\times 4}{2x}$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$6x=\frac{4}{x}$$

Tangohia te \frac{4}{x} mai i ngā taha e rua.

$$6x-\frac{4}{x}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 6x ki te \frac{x}{x}.

$$\frac{6xx}{x}-\frac{4}{x}=0$$

Tā te mea he rite te tauraro o \frac{6xx}{x} me \frac{4}{x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{6xx-4}{x}=0$$

Mahia ngā whakarea i roto o 6xx-4.

$$\frac{6x^{2}-4}{x}=0$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$6x^{2}-4=0$$

Me tāpiri te 4 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$6x^{2}=4$$

Whakawehea ngā taha e rua ki te 6.

$$x^{2}=\frac{4}{6}$$

Whakahekea te hautanga \frac{4}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}=\frac{2}{3}$$

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

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x,x^{2},2x.

$$2x\times 3=2\times 1\times \frac{4}{2x}$$

Whakareatia te 2 ki te 3, ka 6.

$$6x=2\times 1\times \frac{4}{2x}$$

Whakareatia te 2 ki te 1, ka 2.

$$6x=2\times \frac{4}{2x}$$

Tuhia te 2\times \frac{4}{2x} hei hautanga kotahi.

$$6x=\frac{2\times 4}{2x}$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$6x=\frac{4}{x}$$

Tangohia te \frac{4}{x} mai i ngā taha e rua.

$$6x-\frac{4}{x}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 6x ki te \frac{x}{x}.

$$\frac{6xx}{x}-\frac{4}{x}=0$$

Tā te mea he rite te tauraro o \frac{6xx}{x} me \frac{4}{x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{6xx-4}{x}=0$$

Mahia ngā whakarea i roto o 6xx-4.

$$\frac{6x^{2}-4}{x}=0$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$6x^{2}-4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 0 mō b, me -4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-4\right)}}{2\times 6}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-4\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{0±\sqrt{-24\left(-4\right)}}{2\times 6}$$

Whakareatia -24 ki te -4.

$$x=\frac{0±\sqrt{96}}{2\times 6}$$

Tuhia te pūtakerua o te 96.

$$x=\frac{0±4\sqrt{6}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{0±4\sqrt{6}}{12}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{6}}{12} ina he tāpiri te ±.

$$x=\frac{\sqrt{6}}{3}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{6}}{12} ina he tango te ±.

$$x=-\frac{\sqrt{6}}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$