Whakaoti i te 192/x=3x/4

$$\frac { 192 } { x } = \frac { 3 x } { 4 }$$

Whakaoti mō x

$$x=16$$

$$x=-16$$

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 4x, arā, te tauraro pātahi he tino iti rawa te kitea o x,4.

$$4\times 192=x\times 3x$$

Whakareatia te 4 ki te 192, ka 768.

$$768=x\times 3x$$

Whakareatia te x ki te x, ka x^{2}.

$$768=x^{2}\times 3$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}\times 3=768$$

Whakawehea ngā taha e rua ki te 3.

$$x^{2}=\frac{768}{3}$$

Whakawehea te 768 ki te 3, kia riro ko 256.

$$x^{2}=256$$

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

$$x=16 x=-16$$

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 4x, arā, te tauraro pātahi he tino iti rawa te kitea o x,4.

$$4\times 192=x\times 3x$$

Whakareatia te 4 ki te 192, ka 768.

$$768=x\times 3x$$

Whakareatia te x ki te x, ka x^{2}.

$$768=x^{2}\times 3$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}\times 3=768$$

Tangohia te 768 mai i ngā taha e rua.

$$x^{2}\times 3-768=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$3x^{2}-768=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me -768 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-768\right)}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-768\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\left(-768\right)}}{2\times 3}$$

Whakareatia -12 ki te -768.

$$x=\frac{0±\sqrt{9216}}{2\times 3}$$

Tuhia te pūtakerua o te 9216.

$$x=\frac{0±96}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±96}{6}$$

Nā, me whakaoti te whārite x=\frac{0±96}{6} ina he tāpiri te ±. Whakawehe 96 ki te 6.

$$x=16$$

Nā, me whakaoti te whārite x=\frac{0±96}{6} ina he tango te ±. Whakawehe -96 ki te 6.

$$x=-16$$

Kua oti te whārite te whakatau.

$$x=16 x=-16$$