Whakaoti i te 8=4+16-c^2

$$8 = 4 + 16 - c ^ { 2 }$$

Whakaoti mō c

$$c=2\sqrt{3}\approx 3.464101615$$

$$c=-2\sqrt{3}\approx -3.464101615$$

Ngā Upane mā te Kimi Pūtakerua

Tāpirihia te 4 ki te 16, ka 20.

$$8=20-c^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$20-c^{2}=8$$

Tangohia te 20 mai i ngā taha e rua.

$$-c^{2}=8-20$$

Tangohia te 20 i te 8, ka -12.

$$-c^{2}=-12$$

Whakawehea ngā taha e rua ki te -1.

$$c^{2}=\frac{-12}{-1}$$

Ka taea te hautanga \frac{-12}{-1} te whakamāmā ki te 12 mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$c^{2}=12$$

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

$$c=2\sqrt{3} c=-2\sqrt{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 4 ki te 16, ka 20.

$$8=20-c^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$20-c^{2}=8$$

Tangohia te 8 mai i ngā taha e rua.

$$20-c^{2}-8=0$$

Tangohia te 8 i te 20, ka 12.

$$12-c^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$-c^{2}+12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 0 mō b, me 12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 12}}{2\left(-1\right)}$$

Pūrua 0.

$$c=\frac{0±\sqrt{-4\left(-1\right)\times 12}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$c=\frac{0±\sqrt{4\times 12}}{2\left(-1\right)}$$

Whakareatia 4 ki te 12.

$$c=\frac{0±\sqrt{48}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 48.

$$c=\frac{0±4\sqrt{3}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$c=\frac{0±4\sqrt{3}}{-2}$$

Nā, me whakaoti te whārite c=\frac{0±4\sqrt{3}}{-2} ina he tāpiri te ±.

$$c=-2\sqrt{3}$$

Nā, me whakaoti te whārite c=\frac{0±4\sqrt{3}}{-2} ina he tango te ±.

$$c=2\sqrt{3}$$

Kua oti te whārite te whakatau.

$$c=-2\sqrt{3} c=2\sqrt{3}$$