Whakaoti i te -h^2+3h+1=4h-1

$$- h ^ { 2 } + 3 h + 1 = 4 h - 1$$

Whakaoti mō h

$$h=-2$$

$$h=1$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 4h mai i ngā taha e rua.

$$-h^{2}+3h+1-4h=-1$$

Pahekotia te 3h me -4h, ka -h.

$$-h^{2}-h+1=-1$$

Me tāpiri te 1 ki ngā taha e rua.

$$-h^{2}-h+1+1=0$$

Tāpirihia te 1 ki te 1, ka 2.

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

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -h^{2}+ah+bh+2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-1 ab=-2=-2$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=1 b=-2$$

Tuhia anō te -h^{2}-h+2 hei \left(-h^{2}+h\right)+\left(-2h+2\right).

$$\left(-h^{2}+h\right)+\left(-2h+2\right)$$

Tauwehea te h i te tuatahi me te 2 i te rōpū tuarua.

$$h\left(-h+1\right)+2\left(-h+1\right)$$

Whakatauwehea atu te kīanga pātahi -h+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-h+1\right)\left(h+2\right)$$

Hei kimi otinga whārite, me whakaoti te -h+1=0 me te h+2=0.

$$h=1 h=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 4h mai i ngā taha e rua.

$$-h^{2}+3h+1-4h=-1$$

Pahekotia te 3h me -4h, ka -h.

$$-h^{2}-h+1=-1$$

Me tāpiri te 1 ki ngā taha e rua.

$$-h^{2}-h+1+1=0$$

Tāpirihia te 1 ki te 1, ka 2.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, -1 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{-\left(-1\right)±\sqrt{1-4\left(-1\right)\times 2}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$h=\frac{-\left(-1\right)±\sqrt{1+4\times 2}}{2\left(-1\right)}$$

Whakareatia 4 ki te 2.

$$h=\frac{-\left(-1\right)±\sqrt{1+8}}{2\left(-1\right)}$$

Tāpiri 1 ki te 8.

$$h=\frac{-\left(-1\right)±\sqrt{9}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 9.

$$h=\frac{-\left(-1\right)±3}{2\left(-1\right)}$$

Ko te tauaro o -1 ko 1.

$$h=\frac{1±3}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$h=\frac{1±3}{-2}$$

Nā, me whakaoti te whārite h=\frac{1±3}{-2} ina he tāpiri te ±. Tāpiri 1 ki te 3.

$$h=\frac{4}{-2}$$

Whakawehe 4 ki te -2.

$$h=-2$$

Nā, me whakaoti te whārite h=\frac{1±3}{-2} ina he tango te ±. Tango 3 mai i 1.

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

Whakawehe -2 ki te -2.

$$h=1$$

Kua oti te whārite te whakatau.

$$h=-2 h=1$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 4h mai i ngā taha e rua.

$$-h^{2}+3h+1-4h=-1$$

Pahekotia te 3h me -4h, ka -h.

$$-h^{2}-h+1=-1$$

Tangohia te 1 mai i ngā taha e rua.

$$-h^{2}-h=-1-1$$

Tangohia te 1 i te -1, ka -2.

$$-h^{2}-h=-2$$

Whakawehea ngā taha e rua ki te -1.

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

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$h^{2}+\left(-\frac{1}{-1}\right)h=-\frac{2}{-1}$$

Whakawehe -1 ki te -1.

$$h^{2}+h=-\frac{2}{-1}$$

Whakawehe -2 ki te -1.

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

Whakawehea te 1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{2}. Nā, tāpiria te pūrua o te \frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$h^{2}+h+\left(\frac{1}{2}\right)^{2}=2+\left(\frac{1}{2}\right)^{2}$$

Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$h^{2}+h+\frac{1}{4}=2+\frac{1}{4}$$

Tāpiri 2 ki te \frac{1}{4}.

$$h^{2}+h+\frac{1}{4}=\frac{9}{4}$$

Tauwehea h^{2}+h+\frac{1}{4}. 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}.

$$\left(h+\frac{1}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(h+\frac{1}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

$$h+\frac{1}{2}=\frac{3}{2} h+\frac{1}{2}=-\frac{3}{2}$$

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

$$h=1 h=-2$$