Whakaoti i te t^2+4t+1=3

$$t ^ { 2 } + 4 t + 1 = 3$$

Whakaoti mō t

$$t=\sqrt{6}-2\approx 0.449489743$$

$$t=-\sqrt{6}-2\approx -4.449489743$$

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.

$$t^{2}+4t+1=3$$

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

$$t^{2}+4t+1-3=3-3$$

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

$$t^{2}+4t+1-3=0$$

Tango 3 mai i 1.

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

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}.

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

Pūrua 4.

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

Whakareatia -4 ki te -2.

$$t=\frac{-4±\sqrt{16+8}}{2}$$

Tāpiri 16 ki te 8.

$$t=\frac{-4±\sqrt{24}}{2}$$

Tuhia te pūtakerua o te 24.

$$t=\frac{-4±2\sqrt{6}}{2}$$

Nā, me whakaoti te whārite t=\frac{-4±2\sqrt{6}}{2} ina he tāpiri te ±. Tāpiri -4 ki te 2\sqrt{6}.

$$t=\frac{2\sqrt{6}-4}{2}$$

Whakawehe -4+2\sqrt{6} ki te 2.

$$t=\sqrt{6}-2$$

Nā, me whakaoti te whārite t=\frac{-4±2\sqrt{6}}{2} ina he tango te ±. Tango 2\sqrt{6} mai i -4.

$$t=\frac{-2\sqrt{6}-4}{2}$$

Whakawehe -4-2\sqrt{6} ki te 2.

$$t=-\sqrt{6}-2$$

Kua oti te whārite te whakatau.

$$t=\sqrt{6}-2 t=-\sqrt{6}-2$$

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.

$$t^{2}+4t+1=3$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$t^{2}+4t+1-1=3-1$$

Mā te tango i te 1 i a ia ake anō ka toe ko te 0.

$$t^{2}+4t=3-1$$

Tango 1 mai i 3.

$$t^{2}+4t=2$$

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.

$$t^{2}+4t+2^{2}=2+2^{2}$$

Pūrua 2.

$$t^{2}+4t+4=2+4$$

Tāpiri 2 ki te 4.

$$t^{2}+4t+4=6$$

Tauwehea t^{2}+4t+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}.

$$\left(t+2\right)^{2}=6$$

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

$$\sqrt{\left(t+2\right)^{2}}=\sqrt{6}$$

Whakarūnātia.

$$t+2=\sqrt{6} t+2=-\sqrt{6}$$

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

$$t=\sqrt{6}-2 t=-\sqrt{6}-2$$