Whakaoti i te y^2-4y=6

$$y ^ { 2 } - 4 y = 6$$

Whakaoti mō y

$$y=\sqrt{10}+2\approx 5.16227766$$

$$y=2-\sqrt{10}\approx -1.16227766$$

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.

$$y^{2}-4y=6$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$y^{2}-4y-6=6-6$$

Mā te tango i te 6 i a ia ake anō ka toe ko te 0.

$$y^{2}-4y-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -4 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-6\right)}}{2}$$

Pūrua -4.

$$y=\frac{-\left(-4\right)±\sqrt{16-4\left(-6\right)}}{2}$$

Whakareatia -4 ki te -6.

$$y=\frac{-\left(-4\right)±\sqrt{16+24}}{2}$$

Tāpiri 16 ki te 24.

$$y=\frac{-\left(-4\right)±\sqrt{40}}{2}$$

Tuhia te pūtakerua o te 40.

$$y=\frac{-\left(-4\right)±2\sqrt{10}}{2}$$

Ko te tauaro o -4 ko 4.

$$y=\frac{4±2\sqrt{10}}{2}$$

Nā, me whakaoti te whārite y=\frac{4±2\sqrt{10}}{2} ina he tāpiri te ±. Tāpiri 4 ki te 2\sqrt{10}.

$$y=\frac{2\sqrt{10}+4}{2}$$

Whakawehe 4+2\sqrt{10} ki te 2.

$$y=\sqrt{10}+2$$

Nā, me whakaoti te whārite y=\frac{4±2\sqrt{10}}{2} ina he tango te ±. Tango 2\sqrt{10} mai i 4.

$$y=\frac{4-2\sqrt{10}}{2}$$

Whakawehe 4-2\sqrt{10} ki te 2.

$$y=2-\sqrt{10}$$

Kua oti te whārite te whakatau.

$$y=\sqrt{10}+2 y=2-\sqrt{10}$$

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.

$$y^{2}-4y=6$$

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.

$$y^{2}-4y+\left(-2\right)^{2}=6+\left(-2\right)^{2}$$

Pūrua -2.

$$y^{2}-4y+4=6+4$$

Tāpiri 6 ki te 4.

$$y^{2}-4y+4=10$$

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

$$\left(y-2\right)^{2}=10$$

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

$$\sqrt{\left(y-2\right)^{2}}=\sqrt{10}$$

Whakarūnātia.

$$y-2=\sqrt{10} y-2=-\sqrt{10}$$

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

$$y=\sqrt{10}+2 y=2-\sqrt{10}$$