Whakaoti i te 2(x+h-x)^2+3(x+h-x)=5

$$2 ( x + h - x ) ^ { 2 } + 3 ( x + h - x ) = 5$$

Whakaoti mō h

$$h = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

$$h=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te x me -x, ka 0.

$$2h^{2}+3\left(x+h-x\right)=5$$

Pahekotia te x me -x, ka 0.

$$2h^{2}+3h=5$$

Tangohia te 5 mai i ngā taha e rua.

$$2h^{2}+3h-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 3 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{-3±\sqrt{3^{2}-4\times 2\left(-5\right)}}{2\times 2}$$

Pūrua 3.

$$h=\frac{-3±\sqrt{9-4\times 2\left(-5\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$h=\frac{-3±\sqrt{9-8\left(-5\right)}}{2\times 2}$$

Whakareatia -8 ki te -5.

$$h=\frac{-3±\sqrt{9+40}}{2\times 2}$$

Tāpiri 9 ki te 40.

$$h=\frac{-3±\sqrt{49}}{2\times 2}$$

Tuhia te pūtakerua o te 49.

$$h=\frac{-3±7}{2\times 2}$$

Whakareatia 2 ki te 2.

$$h=\frac{-3±7}{4}$$

Nā, me whakaoti te whārite h=\frac{-3±7}{4} ina he tāpiri te ±. Tāpiri -3 ki te 7.

$$h=\frac{4}{4}$$

Whakawehe 4 ki te 4.

$$h=1$$

Nā, me whakaoti te whārite h=\frac{-3±7}{4} ina he tango te ±. Tango 7 mai i -3.

$$h=-\frac{10}{4}$$

Whakahekea te hautanga \frac{-10}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$h=-\frac{5}{2}$$

Kua oti te whārite te whakatau.

$$h=1 h=-\frac{5}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te x me -x, ka 0.

$$2h^{2}+3\left(x+h-x\right)=5$$

Pahekotia te x me -x, ka 0.

$$2h^{2}+3h=5$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2h^{2}+3h}{2}=\frac{5}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$h^{2}+\frac{3}{2}h=\frac{5}{2}$$

Whakawehea te \frac{3}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{4}. Nā, tāpiria te pūrua o te \frac{3}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$h^{2}+\frac{3}{2}h+\left(\frac{3}{4}\right)^{2}=\frac{5}{2}+\left(\frac{3}{4}\right)^{2}$$

Pūruatia \frac{3}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$h^{2}+\frac{3}{2}h+\frac{9}{16}=\frac{5}{2}+\frac{9}{16}$$

Tāpiri \frac{5}{2} ki te \frac{9}{16} 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.

$$h^{2}+\frac{3}{2}h+\frac{9}{16}=\frac{49}{16}$$

Tauwehea h^{2}+\frac{3}{2}h+\frac{9}{16}. 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}.

$$\left(h+\frac{3}{4}\right)^{2}=\frac{49}{16}$$

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

$$\sqrt{\left(h+\frac{3}{4}\right)^{2}}=\sqrt{\frac{49}{16}}$$

Whakarūnātia.

$$h+\frac{3}{4}=\frac{7}{4} h+\frac{3}{4}=-\frac{7}{4}$$

Me tango \frac{3}{4} mai i ngā taha e rua o te whārite.

$$h=1 h=-\frac{5}{2}$$

Whakaoti mō x (complex solution)

$$x\in \mathrm{C}$$

$$h=-\frac{5}{2}\text{ or }h=1$$

Whakaoti mō x

$$x\in \mathrm{R}$$

$$h=1\text{ or }h=-\frac{5}{2}$$