Whakaoti i te k^2-4k+3=0

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

Whakaoti mō k

$$k=1$$

$$k=3$$

Ngā Upane Whakamahi Tauwehe

Hei whakaoti i te whārite, whakatauwehea te k^{2}-4k+3 mā te whakamahi i te tātai k^{2}+\left(a+b\right)k+ab=\left(k+a\right)\left(k+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(k+a\right)\left(k+b\right) mā ngā uara i tātaihia.

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

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

$$k=3 k=1$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei k^{2}+ak+bk+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 k^{2}-4k+3 hei \left(k^{2}-3k\right)+\left(-k+3\right).

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

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

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

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

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

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

$$k=3 k=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

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

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}.

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

Pūrua -4.

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

Whakareatia -4 ki te 3.

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

Tāpiri 16 ki te -12.

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

Tuhia te pūtakerua o te 4.

$$k=\frac{-\left(-4\right)±2}{2}$$

Ko te tauaro o -4 ko 4.

$$k=\frac{4±2}{2}$$

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

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

Whakawehe 6 ki te 2.

$$k=3$$

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

$$k=\frac{2}{2}$$

Whakawehe 2 ki te 2.

$$k=1$$

Kua oti te whārite te whakatau.

$$k=3 k=1$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

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

Me tango 3 mai i ngā taha e rua o te whārite.

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

Mā te tango i te 3 i a ia ake anō ka toe ko te 0.

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

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.

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

Pūrua -2.

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

Tāpiri -3 ki te 4.

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

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

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

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

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

Whakarūnātia.

$$k-2=1 k-2=-1$$

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

$$k=3 k=1$$