Whakaoti i te 3y^2-9=0

$$3 y ^ { 2 } - 9 = 0$$

Whakaoti mō y

$$y=\sqrt{3}\approx 1.732050808$$

$$y=-\sqrt{3}\approx -1.732050808$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 9 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$3y^{2}=9$$

Whakawehea ngā taha e rua ki te 3.

$$y^{2}=\frac{9}{3}$$

Whakawehea te 9 ki te 3, kia riro ko 3.

$$y^{2}=3$$

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

$$y=\sqrt{3} y=-\sqrt{3}$$

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.

$$3y^{2}-9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 3\left(-9\right)}}{2\times 3}$$

Pūrua 0.

$$y=\frac{0±\sqrt{-4\times 3\left(-9\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$y=\frac{0±\sqrt{-12\left(-9\right)}}{2\times 3}$$

Whakareatia -12 ki te -9.

$$y=\frac{0±\sqrt{108}}{2\times 3}$$

Tuhia te pūtakerua o te 108.

$$y=\frac{0±6\sqrt{3}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$y=\frac{0±6\sqrt{3}}{6}$$

Nā, me whakaoti te whārite y=\frac{0±6\sqrt{3}}{6} ina he tāpiri te ±.

$$y=\sqrt{3}$$

Nā, me whakaoti te whārite y=\frac{0±6\sqrt{3}}{6} ina he tango te ±.

$$y=-\sqrt{3}$$

Kua oti te whārite te whakatau.

$$y=\sqrt{3} y=-\sqrt{3}$$