Whakaoti i te f(x)=3x^2-5x-2quad0quadg(x)=2x-7

$$f ( x ) = 3 x ^ { 2 } - 5 x - 2 \quad 0 \quad g ( x ) = 2 x - 7$$

Whakaoti mō x (complex solution)

$$x=\frac{7+\sqrt{35}i}{6}$$

$$x=\frac{-\sqrt{35}i+7}{6}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 2 ki te 0, ka 0.

$$3x^{2}-5x-0gx=2x-7$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$3x^{2}-5x-0=2x-7$$

Tangohia te 2x mai i ngā taha e rua.

$$3x^{2}-5x-0-2x=-7$$

Me tāpiri te 7 ki ngā taha e rua.

$$3x^{2}-5x-0-2x+7=0$$

Whakaraupapatia anō ngā kīanga tau.

$$3x^{2}-5x-2x+7=0$$

Pahekotia te -5x me -2x, ka -7x.

$$3x^{2}-7x+7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -7 mō b, me 7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 3\times 7}}{2\times 3}$$

Pūrua -7.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\times 3\times 7}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-7\right)±\sqrt{49-12\times 7}}{2\times 3}$$

Whakareatia -12 ki te 7.

$$x=\frac{-\left(-7\right)±\sqrt{49-84}}{2\times 3}$$

Tāpiri 49 ki te -84.

$$x=\frac{-\left(-7\right)±\sqrt{-35}}{2\times 3}$$

Tuhia te pūtakerua o te -35.

$$x=\frac{-\left(-7\right)±\sqrt{35}i}{2\times 3}$$

Ko te tauaro o -7 ko 7.

$$x=\frac{7±\sqrt{35}i}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{7±\sqrt{35}i}{6}$$

Nā, me whakaoti te whārite x=\frac{7±\sqrt{35}i}{6} ina he tāpiri te ±. Tāpiri 7 ki te i\sqrt{35}.

$$x=\frac{7+\sqrt{35}i}{6}$$

Nā, me whakaoti te whārite x=\frac{7±\sqrt{35}i}{6} ina he tango te ±. Tango i\sqrt{35} mai i 7.

$$x=\frac{-\sqrt{35}i+7}{6}$$

Kua oti te whārite te whakatau.

$$x=\frac{7+\sqrt{35}i}{6} x=\frac{-\sqrt{35}i+7}{6}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 2 ki te 0, ka 0.

$$3x^{2}-5x-0gx=2x-7$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$3x^{2}-5x-0=2x-7$$

Tangohia te 2x mai i ngā taha e rua.

$$3x^{2}-5x-0-2x=-7$$

Whakaraupapatia anō ngā kīanga tau.

$$3x^{2}-5x-2x=-7$$

Pahekotia te -5x me -2x, ka -7x.

$$3x^{2}-7x=-7$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}-7x}{3}=-\frac{7}{3}$$

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

$$x^{2}-\frac{7}{3}x=-\frac{7}{3}$$

Whakawehea te -\frac{7}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{6}. Nā, tāpiria te pūrua o te -\frac{7}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{7}{3}x+\left(-\frac{7}{6}\right)^{2}=-\frac{7}{3}+\left(-\frac{7}{6}\right)^{2}$$

Pūruatia -\frac{7}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{7}{3}x+\frac{49}{36}=-\frac{7}{3}+\frac{49}{36}$$

Tāpiri -\frac{7}{3} ki te \frac{49}{36} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{7}{3}x+\frac{49}{36}=-\frac{35}{36}$$

Tauwehea x^{2}-\frac{7}{3}x+\frac{49}{36}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{6}\right)^{2}=-\frac{35}{36}$$

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

$$\sqrt{\left(x-\frac{7}{6}\right)^{2}}=\sqrt{-\frac{35}{36}}$$

Whakarūnātia.

$$x-\frac{7}{6}=\frac{\sqrt{35}i}{6} x-\frac{7}{6}=-\frac{\sqrt{35}i}{6}$$

Me tāpiri \frac{7}{6} ki ngā taha e rua o te whārite.

$$x=\frac{7+\sqrt{35}i}{6} x=\frac{-\sqrt{35}i+7}{6}$$

Whakaoti mō g (complex solution)

$$g\in \mathrm{C}$$

$$x=\frac{7+\sqrt{35}i}{6}\text{ or }x=\frac{-\sqrt{35}i+7}{6}$$