Whakaoti i te x^2-4x+2=0

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

Whakaoti mō x

$$x=\sqrt{2}+2\approx 3.414213562$$

$$x=2-\sqrt{2}\approx 0.585786438$$

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.

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

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

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

Pūrua -4.

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

Whakareatia -4 ki te 2.

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

Tāpiri 16 ki te -8.

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

Tuhia te pūtakerua o te 8.

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

Ko te tauaro o -4 ko 4.

$$x=\frac{4±2\sqrt{2}}{2}$$

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

$$x=\frac{2\sqrt{2}+4}{2}$$

Whakawehe 4+2\sqrt{2} ki te 2.

$$x=\sqrt{2}+2$$

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

$$x=\frac{4-2\sqrt{2}}{2}$$

Whakawehe 4-2\sqrt{2} ki te 2.

$$x=2-\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{2}+2 x=2-\sqrt{2}$$

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.

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

Me tango 2 mai i ngā taha e rua o te whārite.

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

Mā te tango i te 2 i a ia ake anō ka toe ko te 0.

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

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.

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

Pūrua -2.

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

Tāpiri -2 ki te 4.

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

Tauwehea te x^{2}-4x+4. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

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

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

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

Whakarūnātia.

$$x-2=\sqrt{2} x-2=-\sqrt{2}$$

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

$$x=\sqrt{2}+2 x=2-\sqrt{2}$$