Whakaoti i te 6n^2-1=-101

$$6 n ^ { 2 } - 1 = - 101$$

Whakaoti mō n

$$n=-\frac{5\sqrt{6}i}{3}\approx -0-4.082482905i$$

$$n=\frac{5\sqrt{6}i}{3}\approx 4.082482905i$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 1 ki ngā taha e rua.

$$6n^{2}=-101+1$$

Tāpirihia te -101 ki te 1, ka -100.

$$6n^{2}=-100$$

Whakawehea ngā taha e rua ki te 6.

$$n^{2}=\frac{-100}{6}$$

Whakahekea te hautanga \frac{-100}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$n^{2}=-\frac{50}{3}$$

Kua oti te whārite te whakatau.

$$n=\frac{5\sqrt{6}i}{3} n=-\frac{5\sqrt{6}i}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 101 ki ngā taha e rua.

$$6n^{2}-1+101=0$$

Tāpirihia te -1 ki te 101, ka 100.

$$6n^{2}+100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 0 mō b, me 100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 6\times 100}}{2\times 6}$$

Pūrua 0.

$$n=\frac{0±\sqrt{-4\times 6\times 100}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$n=\frac{0±\sqrt{-24\times 100}}{2\times 6}$$

Whakareatia -24 ki te 100.

$$n=\frac{0±\sqrt{-2400}}{2\times 6}$$

Tuhia te pūtakerua o te -2400.

$$n=\frac{0±20\sqrt{6}i}{2\times 6}$$

Whakareatia 2 ki te 6.

$$n=\frac{0±20\sqrt{6}i}{12}$$

Nā, me whakaoti te whārite n=\frac{0±20\sqrt{6}i}{12} ina he tāpiri te ±.

$$n=\frac{5\sqrt{6}i}{3}$$

Nā, me whakaoti te whārite n=\frac{0±20\sqrt{6}i}{12} ina he tango te ±.

$$n=-\frac{5\sqrt{6}i}{3}$$

Kua oti te whārite te whakatau.

$$n=\frac{5\sqrt{6}i}{3} n=-\frac{5\sqrt{6}i}{3}$$