Whakaoti i te 64-x^2=x^2

$$64- { x }^{ 2 } = { x }^{ 2 }$$

Whakaoti mō x

$$x=4\sqrt{2}\approx 5.656854249$$

$$x=-4\sqrt{2}\approx -5.656854249$$

Ngā Upane mā te Kimi Pūtakerua

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

$$64-x^{2}-x^{2}=0$$

Pahekotia te -x^{2} me -x^{2}, ka -2x^{2}.

$$64-2x^{2}=0$$

Tangohia te 64 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-2x^{2}=-64$$

Whakawehea ngā taha e rua ki te -2.

$$x^{2}=\frac{-64}{-2}$$

Whakawehea te -64 ki te -2, kia riro ko 32.

$$x^{2}=32$$

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

$$x=4\sqrt{2} x=-4\sqrt{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$64-x^{2}-x^{2}=0$$

Pahekotia te -x^{2} me -x^{2}, ka -2x^{2}.

$$64-2x^{2}=0$$

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.

$$-2x^{2}+64=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 0 mō b, me 64 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 64}}{2\left(-2\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 64}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{0±\sqrt{8\times 64}}{2\left(-2\right)}$$

Whakareatia 8 ki te 64.

$$x=\frac{0±\sqrt{512}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 512.

$$x=\frac{0±16\sqrt{2}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{0±16\sqrt{2}}{-4}$$

Nā, me whakaoti te whārite x=\frac{0±16\sqrt{2}}{-4} ina he tāpiri te ±.

$$x=-4\sqrt{2}$$

Nā, me whakaoti te whārite x=\frac{0±16\sqrt{2}}{-4} ina he tango te ±.

$$x=4\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=-4\sqrt{2} x=4\sqrt{2}$$