Whakaoti i te m^2-2m-3=1

$$m ^ { 2 } - 2 m - 3 = 1$$

Whakaoti mō m

$$m=\sqrt{5}+1\approx 3.236067977$$

$$m=1-\sqrt{5}\approx -1.236067977$$

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.

$$m^{2}-2m-3=1$$

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

$$m^{2}-2m-3-1=1-1$$

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

$$m^{2}-2m-3-1=0$$

Tango 1 mai i -3.

$$m^{2}-2m-4=0$$

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

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

Pūrua -2.

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

Whakareatia -4 ki te -4.

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

Tāpiri 4 ki te 16.

$$m=\frac{-\left(-2\right)±\sqrt{20}}{2}$$

Tuhia te pūtakerua o te 20.

$$m=\frac{-\left(-2\right)±2\sqrt{5}}{2}$$

Ko te tauaro o -2 ko 2.

$$m=\frac{2±2\sqrt{5}}{2}$$

Nā, me whakaoti te whārite m=\frac{2±2\sqrt{5}}{2} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{5}.

$$m=\frac{2\sqrt{5}+2}{2}$$

Whakawehe 2+2\sqrt{5} ki te 2.

$$m=\sqrt{5}+1$$

Nā, me whakaoti te whārite m=\frac{2±2\sqrt{5}}{2} ina he tango te ±. Tango 2\sqrt{5} mai i 2.

$$m=\frac{2-2\sqrt{5}}{2}$$

Whakawehe 2-2\sqrt{5} ki te 2.

$$m=1-\sqrt{5}$$

Kua oti te whārite te whakatau.

$$m=\sqrt{5}+1 m=1-\sqrt{5}$$

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.

$$m^{2}-2m-3=1$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$m^{2}-2m-3-\left(-3\right)=1-\left(-3\right)$$

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

$$m^{2}-2m=1-\left(-3\right)$$

Tango -3 mai i 1.

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

Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Tāpiri 4 ki te 1.

$$m^{2}-2m+1=5$$

Tauwehea m^{2}-2m+1. 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}.

$$\left(m-1\right)^{2}=5$$

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

$$\sqrt{\left(m-1\right)^{2}}=\sqrt{5}$$

Whakarūnātia.

$$m-1=\sqrt{5} m-1=-\sqrt{5}$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$m=\sqrt{5}+1 m=1-\sqrt{5}$$