Whakaoti i te a^2-10a=4

$$a ^ { 2 } - 10 a = 4$$

Whakaoti mō a

$$a=\sqrt{29}+5\approx 10.385164807$$

$$a=5-\sqrt{29}\approx -0.385164807$$

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.

$$a^{2}-10a=4$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$a^{2}-10a-4=4-4$$

Mā te tango i te 4 i a ia ake anō ka toe ko te 0.

$$a^{2}-10a-4=0$$

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

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

Pūrua -10.

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

Whakareatia -4 ki te -4.

$$a=\frac{-\left(-10\right)±\sqrt{100+16}}{2}$$

Tāpiri 100 ki te 16.

$$a=\frac{-\left(-10\right)±\sqrt{116}}{2}$$

Tuhia te pūtakerua o te 116.

$$a=\frac{-\left(-10\right)±2\sqrt{29}}{2}$$

Ko te tauaro o -10 ko 10.

$$a=\frac{10±2\sqrt{29}}{2}$$

Nā, me whakaoti te whārite a=\frac{10±2\sqrt{29}}{2} ina he tāpiri te ±. Tāpiri 10 ki te 2\sqrt{29}.

$$a=\frac{2\sqrt{29}+10}{2}$$

Whakawehe 10+2\sqrt{29} ki te 2.

$$a=\sqrt{29}+5$$

Nā, me whakaoti te whārite a=\frac{10±2\sqrt{29}}{2} ina he tango te ±. Tango 2\sqrt{29} mai i 10.

$$a=\frac{10-2\sqrt{29}}{2}$$

Whakawehe 10-2\sqrt{29} ki te 2.

$$a=5-\sqrt{29}$$

Kua oti te whārite te whakatau.

$$a=\sqrt{29}+5 a=5-\sqrt{29}$$

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.

$$a^{2}-10a=4$$

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.

$$a^{2}-10a+\left(-5\right)^{2}=4+\left(-5\right)^{2}$$

Pūrua -5.

$$a^{2}-10a+25=4+25$$

Tāpiri 4 ki te 25.

$$a^{2}-10a+25=29$$

Tauwehea a^{2}-10a+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}.

$$\left(a-5\right)^{2}=29$$

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

$$\sqrt{\left(a-5\right)^{2}}=\sqrt{29}$$

Whakarūnātia.

$$a-5=\sqrt{29} a-5=-\sqrt{29}$$

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

$$a=\sqrt{29}+5 a=5-\sqrt{29}$$