Whakaoti i te 9-x^2=1

$$9 - x ^ { 2 } = 1$$

Whakaoti mō x

$$x=2\sqrt{2}\approx 2.828427125$$

$$x=-2\sqrt{2}\approx -2.828427125$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 9 mai i ngā taha e rua.

$$-x^{2}=1-9$$

Tangohia te 9 i te 1, ka -8.

$$-x^{2}=-8$$

Whakawehea ngā taha e rua ki te -1.

$$x^{2}=\frac{-8}{-1}$$

Ka taea te hautanga \frac{-8}{-1} te whakamāmā ki te 8 mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x^{2}=8$$

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

$$x=2\sqrt{2} x=-2\sqrt{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 1 mai i ngā taha e rua.

$$9-x^{2}-1=0$$

Tangohia te 1 i te 9, ka 8.

$$8-x^{2}=0$$

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.

$$-x^{2}+8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 0 mō b, me 8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{0±\sqrt{4\times 8}}{2\left(-1\right)}$$

Whakareatia 4 ki te 8.

$$x=\frac{0±\sqrt{32}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 32.

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

Whakareatia 2 ki te -1.

$$x=\frac{0±4\sqrt{2}}{-2}$$

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

$$x=-2\sqrt{2}$$

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

$$x=2\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=-2\sqrt{2} x=2\sqrt{2}$$