Whakaoti i te 2/3=b^2-1/4b

$$\frac { 2 } { 3 } = \frac { b ^ { 2 } - 1 } { 4 b }$$

Whakaoti mō b

$$b=-\frac{1}{3}\approx -0.333333333$$

$$b=3$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tē taea kia ōrite te tāupe b ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 12b, arā, te tauraro pātahi he tino iti rawa te kitea o 3,4b.

$$8b=3\left(b^{2}-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te b^{2}-1.

$$8b=3b^{2}-3$$

Tangohia te 3b^{2} mai i ngā taha e rua.

$$8b-3b^{2}=-3$$

Me tāpiri te 3 ki ngā taha e rua.

$$8b-3b^{2}+3=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-3b^{2}+8b+3=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -3b^{2}+ab+bb+3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=8 ab=-3\times 3=-9$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -9.

$$-1,9 -3,3$$

Tātaihia te tapeke mō ia takirua.

$$-1+9=8 -3+3=0$$

Ko te otinga te takirua ka hoatu i te tapeke 8.

$$a=9 b=-1$$

Tuhia anō te -3b^{2}+8b+3 hei \left(-3b^{2}+9b\right)+\left(-b+3\right).

$$\left(-3b^{2}+9b\right)+\left(-b+3\right)$$

Whakatauwehea atu 3b i te -3b^{2}+9b.

$$3b\left(-b+3\right)-b+3$$

Whakatauwehea atu te kīanga pātahi -b+3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-b+3\right)\left(3b+1\right)$$

Hei kimi otinga whārite, me whakaoti te -b+3=0 me te 3b+1=0.

$$b=3 b=-\frac{1}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe b ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 12b, arā, te tauraro pātahi he tino iti rawa te kitea o 3,4b.

$$8b=3\left(b^{2}-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te b^{2}-1.

$$8b=3b^{2}-3$$

Tangohia te 3b^{2} mai i ngā taha e rua.

$$8b-3b^{2}=-3$$

Me tāpiri te 3 ki ngā taha e rua.

$$8b-3b^{2}+3=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-3b^{2}+8b+3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, 8 mō b, me 3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-8±\sqrt{8^{2}-4\left(-3\right)\times 3}}{2\left(-3\right)}$$

Pūrua 8.

$$b=\frac{-8±\sqrt{64-4\left(-3\right)\times 3}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$b=\frac{-8±\sqrt{64+12\times 3}}{2\left(-3\right)}$$

Whakareatia 12 ki te 3.

$$b=\frac{-8±\sqrt{64+36}}{2\left(-3\right)}$$

Tāpiri 64 ki te 36.

$$b=\frac{-8±\sqrt{100}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 100.

$$b=\frac{-8±10}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$b=\frac{-8±10}{-6}$$

Nā, me whakaoti te whārite b=\frac{-8±10}{-6} ina he tāpiri te ±. Tāpiri -8 ki te 10.

$$b=\frac{2}{-6}$$

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

$$b=-\frac{1}{3}$$

Nā, me whakaoti te whārite b=\frac{-8±10}{-6} ina he tango te ±. Tango 10 mai i -8.

$$b=-\frac{18}{-6}$$

Whakawehe -18 ki te -6.

$$b=3$$

Kua oti te whārite te whakatau.

$$b=-\frac{1}{3} b=3$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe b ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 12b, arā, te tauraro pātahi he tino iti rawa te kitea o 3,4b.

$$8b=3\left(b^{2}-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te b^{2}-1.

$$8b=3b^{2}-3$$

Tangohia te 3b^{2} mai i ngā taha e rua.

$$8b-3b^{2}=-3$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-3b^{2}+8b=-3$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3b^{2}+8b}{-3}=-\frac{3}{-3}$$

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

$$b^{2}+\frac{8}{-3}b=-\frac{3}{-3}$$

Whakawehe 8 ki te -3.

$$b^{2}-\frac{8}{3}b=-\frac{3}{-3}$$

Whakawehe -3 ki te -3.

$$b^{2}-\frac{8}{3}b=1$$

Whakawehea te -\frac{8}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{4}{3}. Nā, tāpiria te pūrua o te -\frac{4}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$b^{2}-\frac{8}{3}b+\left(-\frac{4}{3}\right)^{2}=1+\left(-\frac{4}{3}\right)^{2}$$

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

$$b^{2}-\frac{8}{3}b+\frac{16}{9}=1+\frac{16}{9}$$

Tāpiri 1 ki te \frac{16}{9}.

$$b^{2}-\frac{8}{3}b+\frac{16}{9}=\frac{25}{9}$$

Tauwehea b^{2}-\frac{8}{3}b+\frac{16}{9}. 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}.

$$\left(b-\frac{4}{3}\right)^{2}=\frac{25}{9}$$

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

$$\sqrt{\left(b-\frac{4}{3}\right)^{2}}=\sqrt{\frac{25}{9}}$$

Whakarūnātia.

$$b-\frac{4}{3}=\frac{5}{3} b-\frac{4}{3}=-\frac{5}{3}$$

Me tāpiri \frac{4}{3} ki ngā taha e rua o te whārite.

$$b=3 b=-\frac{1}{3}$$