Whakaoti i te 2(2u^2-4u)+3=0

$$2 ( 2 u ^ { 2 } - 4 u ) + 3 = 0$$

Whakaoti mō u

$$u=\frac{1}{2}=0.5$$

$$u = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 2u^{2}-4u.

$$4u^{2}-8u+3=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 4u^{2}+au+bu+3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-8 ab=4\times 3=12$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 12.

$$-1,-12 -2,-6 -3,-4$$

Tātaihia te tapeke mō ia takirua.

$$-1-12=-13 -2-6=-8 -3-4=-7$$

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

$$a=-6 b=-2$$

Tuhia anō te 4u^{2}-8u+3 hei \left(4u^{2}-6u\right)+\left(-2u+3\right).

$$\left(4u^{2}-6u\right)+\left(-2u+3\right)$$

Tauwehea te 2u i te tuatahi me te -1 i te rōpū tuarua.

$$2u\left(2u-3\right)-\left(2u-3\right)$$

Whakatauwehea atu te kīanga pātahi 2u-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2u-3\right)\left(2u-1\right)$$

Hei kimi otinga whārite, me whakaoti te 2u-3=0 me te 2u-1=0.

$$u=\frac{3}{2} u=\frac{1}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 2u^{2}-4u.

$$4u^{2}-8u+3=0$$

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

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

Pūrua -8.

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

Whakareatia -4 ki te 4.

$$u=\frac{-\left(-8\right)±\sqrt{64-16\times 3}}{2\times 4}$$

Whakareatia -16 ki te 3.

$$u=\frac{-\left(-8\right)±\sqrt{64-48}}{2\times 4}$$

Tāpiri 64 ki te -48.

$$u=\frac{-\left(-8\right)±\sqrt{16}}{2\times 4}$$

Tuhia te pūtakerua o te 16.

$$u=\frac{-\left(-8\right)±4}{2\times 4}$$

Ko te tauaro o -8 ko 8.

$$u=\frac{8±4}{2\times 4}$$

Whakareatia 2 ki te 4.

$$u=\frac{8±4}{8}$$

Nā, me whakaoti te whārite u=\frac{8±4}{8} ina he tāpiri te ±. Tāpiri 8 ki te 4.

$$u=\frac{12}{8}$$

Whakahekea te hautanga \frac{12}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$u=\frac{3}{2}$$

Nā, me whakaoti te whārite u=\frac{8±4}{8} ina he tango te ±. Tango 4 mai i 8.

$$u=\frac{4}{8}$$

Whakahekea te hautanga \frac{4}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$u=\frac{1}{2}$$

Kua oti te whārite te whakatau.

$$u=\frac{3}{2} u=\frac{1}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 2u^{2}-4u.

$$4u^{2}-8u+3=0$$

Tangohia te 3 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$4u^{2}-8u=-3$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4u^{2}-8u}{4}=-\frac{3}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

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

Whakawehe -8 ki te 4.

$$u^{2}-2u=-\frac{3}{4}$$

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

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

Tāpiri -\frac{3}{4} ki te 1.

$$u^{2}-2u+1=\frac{1}{4}$$

Tauwehea u^{2}-2u+1. 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}.

$$\left(u-1\right)^{2}=\frac{1}{4}$$

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

$$\sqrt{\left(u-1\right)^{2}}=\sqrt{\frac{1}{4}}$$

Whakarūnātia.

$$u-1=\frac{1}{2} u-1=-\frac{1}{2}$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$u=\frac{3}{2} u=\frac{1}{2}$$