Whakaoti i te m^2-13m+72=0

$${ m }^{ 2 } -13m+72=0$$

Whakaoti mō m

$$m=\frac{13+\sqrt{119}i}{2}\approx 6.5+5.454356057i$$

$$m=\frac{-\sqrt{119}i+13}{2}\approx 6.5-5.454356057i$$

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.

$$m^{2}-13m+72=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -13 mō b, me 72 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 72}}{2}$$

Pūrua -13.

$$m=\frac{-\left(-13\right)±\sqrt{169-4\times 72}}{2}$$

Whakareatia -4 ki te 72.

$$m=\frac{-\left(-13\right)±\sqrt{169-288}}{2}$$

Tāpiri 169 ki te -288.

$$m=\frac{-\left(-13\right)±\sqrt{-119}}{2}$$

Tuhia te pūtakerua o te -119.

$$m=\frac{-\left(-13\right)±\sqrt{119}i}{2}$$

Ko te tauaro o -13 ko 13.

$$m=\frac{13±\sqrt{119}i}{2}$$

Nā, me whakaoti te whārite m=\frac{13±\sqrt{119}i}{2} ina he tāpiri te ±. Tāpiri 13 ki te i\sqrt{119}.

$$m=\frac{13+\sqrt{119}i}{2}$$

Nā, me whakaoti te whārite m=\frac{13±\sqrt{119}i}{2} ina he tango te ±. Tango i\sqrt{119} mai i 13.

$$m=\frac{-\sqrt{119}i+13}{2}$$

Kua oti te whārite te whakatau.

$$m=\frac{13+\sqrt{119}i}{2} m=\frac{-\sqrt{119}i+13}{2}$$

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.

$$m^{2}-13m+72=0$$

Me tango 72 mai i ngā taha e rua o te whārite.

$$m^{2}-13m+72-72=-72$$

Mā te tango i te 72 i a ia ake anō ka toe ko te 0.

$$m^{2}-13m=-72$$

Whakawehea te -13, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{13}{2}. Nā, tāpiria te pūrua o te -\frac{13}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$m^{2}-13m+\left(-\frac{13}{2}\right)^{2}=-72+\left(-\frac{13}{2}\right)^{2}$$

Pūruatia -\frac{13}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$m^{2}-13m+\frac{169}{4}=-72+\frac{169}{4}$$

Tāpiri -72 ki te \frac{169}{4}.

$$m^{2}-13m+\frac{169}{4}=-\frac{119}{4}$$

Tauwehea m^{2}-13m+\frac{169}{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}.

$$\left(m-\frac{13}{2}\right)^{2}=-\frac{119}{4}$$

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

$$\sqrt{\left(m-\frac{13}{2}\right)^{2}}=\sqrt{-\frac{119}{4}}$$

Whakarūnātia.

$$m-\frac{13}{2}=\frac{\sqrt{119}i}{2} m-\frac{13}{2}=-\frac{\sqrt{119}i}{2}$$

Me tāpiri \frac{13}{2} ki ngā taha e rua o te whārite.

$$m=\frac{13+\sqrt{119}i}{2} m=\frac{-\sqrt{119}i+13}{2}$$