Whakaoti i te n^2-8=113?quadn^2-105

$$n ^ { 2 } - 8 = 113 ? \quad n ^ { 2 } - 105$$

Whakaoti mō n

$$n=\frac{\sqrt{679}}{28}\approx 0.930629587$$

$$n=-\frac{\sqrt{679}}{28}\approx -0.930629587$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 113n^{2} mai i ngā taha e rua.

$$n^{2}-8-113n^{2}=-105$$

Pahekotia te n^{2} me -113n^{2}, ka -112n^{2}.

$$-112n^{2}-8=-105$$

Me tāpiri te 8 ki ngā taha e rua.

$$-112n^{2}=-105+8$$

Tāpirihia te -105 ki te 8, ka -97.

$$-112n^{2}=-97$$

Whakawehea ngā taha e rua ki te -112.

$$n^{2}=\frac{-97}{-112}$$

Ka taea te hautanga \frac{-97}{-112} te whakamāmā ki te \frac{97}{112} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$n^{2}=\frac{97}{112}$$

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

$$n=\frac{\sqrt{679}}{28} n=-\frac{\sqrt{679}}{28}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 113n^{2} mai i ngā taha e rua.

$$n^{2}-8-113n^{2}=-105$$

Pahekotia te n^{2} me -113n^{2}, ka -112n^{2}.

$$-112n^{2}-8=-105$$

Me tāpiri te 105 ki ngā taha e rua.

$$-112n^{2}-8+105=0$$

Tāpirihia te -8 ki te 105, ka 97.

$$-112n^{2}+97=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -112 mō a, 0 mō b, me 97 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-112\right)\times 97}}{2\left(-112\right)}$$

Pūrua 0.

$$n=\frac{0±\sqrt{-4\left(-112\right)\times 97}}{2\left(-112\right)}$$

Whakareatia -4 ki te -112.

$$n=\frac{0±\sqrt{448\times 97}}{2\left(-112\right)}$$

Whakareatia 448 ki te 97.

$$n=\frac{0±\sqrt{43456}}{2\left(-112\right)}$$

Tuhia te pūtakerua o te 43456.

$$n=\frac{0±8\sqrt{679}}{2\left(-112\right)}$$

Whakareatia 2 ki te -112.

$$n=\frac{0±8\sqrt{679}}{-224}$$

Nā, me whakaoti te whārite n=\frac{0±8\sqrt{679}}{-224} ina he tāpiri te ±.

$$n=-\frac{\sqrt{679}}{28}$$

Nā, me whakaoti te whārite n=\frac{0±8\sqrt{679}}{-224} ina he tango te ±.

$$n=\frac{\sqrt{679}}{28}$$

Kua oti te whārite te whakatau.

$$n=-\frac{\sqrt{679}}{28} n=\frac{\sqrt{679}}{28}$$