Whakaoti i te -(x-1)(-x+3)=0

$$- ( x - 1 ) ( - x + 3 ) = 0$$

Whakaoti mō x

$$x=3$$

$$x=1$$

Ngā Upane Whakamahi Tauwehe

Hei kimi i te tauaro o x-1, kimihia te tauaro o ia taurangi.

$$\left(-x-\left(-1\right)\right)\left(-x+3\right)=0$$

Ko te tauaro o -1 ko 1.

$$\left(-x+1\right)\left(-x+3\right)=0$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o -x+1 ki ia tau o -x+3.

$$-x\left(-x\right)-3x-x+3=0$$

Whakareatia te -1 ki te -1, ka 1.

$$xx-3x-x+3=0$$

Whakareatia te x ki te x, ka x^{2}.

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

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

$$x^{2}-4x+3=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}-4x+3 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-4 ab=3$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-3 b=-1$$

Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.

$$\left(x-3\right)\left(x-1\right)$$

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

$$x=3 x=1$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Hei kimi i te tauaro o x-1, kimihia te tauaro o ia taurangi.

$$\left(-x-\left(-1\right)\right)\left(-x+3\right)=0$$

Ko te tauaro o -1 ko 1.

$$\left(-x+1\right)\left(-x+3\right)=0$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o -x+1 ki ia tau o -x+3.

$$-x\left(-x\right)-3x-x+3=0$$

Whakareatia te -1 ki te -1, ka 1.

$$xx-3x-x+3=0$$

Whakareatia te x ki te x, ka x^{2}.

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

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

$$x^{2}-4x+3=0$$

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

$$a+b=-4 ab=1\times 3=3$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-3 b=-1$$

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

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

Tauwehea te x i te tuatahi me te -1 i te rōpū tuarua.

$$x\left(x-3\right)-\left(x-3\right)$$

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

$$\left(x-3\right)\left(x-1\right)$$

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

$$x=3 x=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Hei kimi i te tauaro o x-1, kimihia te tauaro o ia taurangi.

$$\left(-x-\left(-1\right)\right)\left(-x+3\right)=0$$

Ko te tauaro o -1 ko 1.

$$\left(-x+1\right)\left(-x+3\right)=0$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o -x+1 ki ia tau o -x+3.

$$-x\left(-x\right)-3x-x+3=0$$

Whakareatia te -1 ki te -1, ka 1.

$$xx-3x-x+3=0$$

Whakareatia te x ki te x, ka x^{2}.

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

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

$$x^{2}-4x+3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -4 mō b, me 3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua -4.

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

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-4\right)±\sqrt{16-12}}{2}$$

Tāpiri 16 ki te -12.

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

Tuhia te pūtakerua o te 4.

$$x=\frac{-\left(-4\right)±2}{2}$$

Ko te tauaro o -4 ko 4.

$$x=\frac{4±2}{2}$$

Nā, me whakaoti te whārite x=\frac{4±2}{2} ina he tāpiri te ±. Tāpiri 4 ki te 2.

$$x=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{4±2}{2} ina he tango te ±. Tango 2 mai i 4.

$$x=\frac{2}{2}$$

Whakawehe 2 ki te 2.

$$x=1$$

Kua oti te whārite te whakatau.

$$x=3 x=1$$

Ngā Upane mō te Whakaoti i te Pūrua

Hei kimi i te tauaro o x-1, kimihia te tauaro o ia taurangi.

$$\left(-x-\left(-1\right)\right)\left(-x+3\right)=0$$

Ko te tauaro o -1 ko 1.

$$\left(-x+1\right)\left(-x+3\right)=0$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o -x+1 ki ia tau o -x+3.

$$-x\left(-x\right)-3x-x+3=0$$

Whakareatia te -1 ki te -1, ka 1.

$$xx-3x-x+3=0$$

Whakareatia te x ki te x, ka x^{2}.

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

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

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

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

$$x^{2}-4x=-3$$

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

$$x^{2}-4x+\left(-2\right)^{2}=-3+\left(-2\right)^{2}$$

Pūrua -2.

$$x^{2}-4x+4=-3+4$$

Tāpiri -3 ki te 4.

$$x^{2}-4x+4=1$$

Tauwehea x^{2}-4x+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}.

$$\left(x-2\right)^{2}=1$$

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

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{1}$$

Whakarūnātia.

$$x-2=1 x-2=-1$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$x=3 x=1$$