Whakaoti i te q^2-10q+5=0

$$q ^ { 2 } - 10 q + 5 = 0$$

Whakaoti mō q

$$q=2\sqrt{5}+5\approx 9.472135955$$

$$q=5-2\sqrt{5}\approx 0.527864045$$

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.

$$q^{2}-10q+5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -10 mō b, me 5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 5}}{2}$$

Pūrua -10.

$$q=\frac{-\left(-10\right)±\sqrt{100-4\times 5}}{2}$$

Whakareatia -4 ki te 5.

$$q=\frac{-\left(-10\right)±\sqrt{100-20}}{2}$$

Tāpiri 100 ki te -20.

$$q=\frac{-\left(-10\right)±\sqrt{80}}{2}$$

Tuhia te pūtakerua o te 80.

$$q=\frac{-\left(-10\right)±4\sqrt{5}}{2}$$

Ko te tauaro o -10 ko 10.

$$q=\frac{10±4\sqrt{5}}{2}$$

Nā, me whakaoti te whārite q=\frac{10±4\sqrt{5}}{2} ina he tāpiri te ±. Tāpiri 10 ki te 4\sqrt{5}.

$$q=\frac{4\sqrt{5}+10}{2}$$

Whakawehe 10+4\sqrt{5} ki te 2.

$$q=2\sqrt{5}+5$$

Nā, me whakaoti te whārite q=\frac{10±4\sqrt{5}}{2} ina he tango te ±. Tango 4\sqrt{5} mai i 10.

$$q=\frac{10-4\sqrt{5}}{2}$$

Whakawehe 10-4\sqrt{5} ki te 2.

$$q=5-2\sqrt{5}$$

Kua oti te whārite te whakatau.

$$q=2\sqrt{5}+5 q=5-2\sqrt{5}$$

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.

$$q^{2}-10q+5=0$$

Me tango 5 mai i ngā taha e rua o te whārite.

$$q^{2}-10q+5-5=-5$$

Mā te tango i te 5 i a ia ake anō ka toe ko te 0.

$$q^{2}-10q=-5$$

Whakawehea te -10, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -5. Nā, tāpiria te pūrua o te -5 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$q^{2}-10q+\left(-5\right)^{2}=-5+\left(-5\right)^{2}$$

Pūrua -5.

$$q^{2}-10q+25=-5+25$$

Tāpiri -5 ki te 25.

$$q^{2}-10q+25=20$$

Tauwehea q^{2}-10q+25. 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}.

$$\left(q-5\right)^{2}=20$$

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

$$\sqrt{\left(q-5\right)^{2}}=\sqrt{20}$$

Whakarūnātia.

$$q-5=2\sqrt{5} q-5=-2\sqrt{5}$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$q=2\sqrt{5}+5 q=5-2\sqrt{5}$$