Whakaoti i te 2n^2-5n-4=6

$$2 n ^ { 2 } - 5 n - 4 = 6$$

Whakaoti mō n

$$n = \frac{\sqrt{105} + 5}{4} \approx 3.811737691$$

$$n=\frac{5-\sqrt{105}}{4}\approx -1.311737691$$

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.

$$2n^{2}-5n-4=6$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$2n^{2}-5n-4-6=6-6$$

Mā te tango i te 6 i a ia ake anō ka toe ko te 0.

$$2n^{2}-5n-4-6=0$$

Tango 6 mai i -4.

$$2n^{2}-5n-10=0$$

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

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

Pūrua -5.

$$n=\frac{-\left(-5\right)±\sqrt{25-4\times 2\left(-10\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$n=\frac{-\left(-5\right)±\sqrt{25-8\left(-10\right)}}{2\times 2}$$

Whakareatia -8 ki te -10.

$$n=\frac{-\left(-5\right)±\sqrt{25+80}}{2\times 2}$$

Tāpiri 25 ki te 80.

$$n=\frac{-\left(-5\right)±\sqrt{105}}{2\times 2}$$

Ko te tauaro o -5 ko 5.

$$n=\frac{5±\sqrt{105}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$n=\frac{5±\sqrt{105}}{4}$$

Nā, me whakaoti te whārite n=\frac{5±\sqrt{105}}{4} ina he tāpiri te ±. Tāpiri 5 ki te \sqrt{105}.

$$n=\frac{\sqrt{105}+5}{4}$$

Nā, me whakaoti te whārite n=\frac{5±\sqrt{105}}{4} ina he tango te ±. Tango \sqrt{105} mai i 5.

$$n=\frac{5-\sqrt{105}}{4}$$

Kua oti te whārite te whakatau.

$$n=\frac{\sqrt{105}+5}{4} n=\frac{5-\sqrt{105}}{4}$$

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.

$$2n^{2}-5n-4=6$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$2n^{2}-5n-4-\left(-4\right)=6-\left(-4\right)$$

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

$$2n^{2}-5n=6-\left(-4\right)$$

Tango -4 mai i 6.

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

Whakawehea ngā taha e rua ki te 2.

$$\frac{2n^{2}-5n}{2}=\frac{10}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$n^{2}-\frac{5}{2}n=\frac{10}{2}$$

Whakawehe 10 ki te 2.

$$n^{2}-\frac{5}{2}n=5$$

Whakawehea te -\frac{5}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{4}. Nā, tāpiria te pūrua o te -\frac{5}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$n^{2}-\frac{5}{2}n+\left(-\frac{5}{4}\right)^{2}=5+\left(-\frac{5}{4}\right)^{2}$$

Pūruatia -\frac{5}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$n^{2}-\frac{5}{2}n+\frac{25}{16}=5+\frac{25}{16}$$

Tāpiri 5 ki te \frac{25}{16}.

$$n^{2}-\frac{5}{2}n+\frac{25}{16}=\frac{105}{16}$$

Tauwehea n^{2}-\frac{5}{2}n+\frac{25}{16}. 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}.

$$\left(n-\frac{5}{4}\right)^{2}=\frac{105}{16}$$

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

$$\sqrt{\left(n-\frac{5}{4}\right)^{2}}=\sqrt{\frac{105}{16}}$$

Whakarūnātia.

$$n-\frac{5}{4}=\frac{\sqrt{105}}{4} n-\frac{5}{4}=-\frac{\sqrt{105}}{4}$$

Me tāpiri \frac{5}{4} ki ngā taha e rua o te whārite.

$$n=\frac{\sqrt{105}+5}{4} n=\frac{5-\sqrt{105}}{4}$$