Whakaoti i te 9x^2-4=0

$$9 { x }^{ 2 } -4=0$$

Whakaoti mō x

$$x=\frac{2}{3}\approx 0.666666667$$

$$x=-\frac{2}{3}\approx -0.666666667$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakaarohia te 9x^{2}-4. Tuhia anō te 9x^{2}-4 hei \left(3x\right)^{2}-2^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-2\right)\left(3x+2\right)=0$$

Hei kimi otinga whārite, me whakaoti te 3x-2=0 me te 3x+2=0.

$$x=\frac{2}{3} x=-\frac{2}{3}$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 4 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$9x^{2}=4$$

Whakawehea ngā taha e rua ki te 9.

$$x^{2}=\frac{4}{9}$$

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

$$x=\frac{2}{3} x=-\frac{2}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$9x^{2}-4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, 0 mō b, me -4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-4\right)}}{2\times 9}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-4\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{0±\sqrt{-36\left(-4\right)}}{2\times 9}$$

Whakareatia -36 ki te -4.

$$x=\frac{0±\sqrt{144}}{2\times 9}$$

Tuhia te pūtakerua o te 144.

$$x=\frac{0±12}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{0±12}{18}$$

Nā, me whakaoti te whārite x=\frac{0±12}{18} ina he tāpiri te ±. Whakahekea te hautanga \frac{12}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x=\frac{2}{3}$$

Nā, me whakaoti te whārite x=\frac{0±12}{18} ina he tango te ±. Whakahekea te hautanga \frac{-12}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x=-\frac{2}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{2}{3} x=-\frac{2}{3}$$