Whakaoti i te 36y^2+40=0

$$36 { y }^{ 2 } +40 = 0$$

Whakaoti mō y

$$y=-\frac{\sqrt{10}i}{3}\approx -0-1.054092553i$$

$$y=\frac{\sqrt{10}i}{3}\approx 1.054092553i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 40 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$36y^{2}=-40$$

Whakawehea ngā taha e rua ki te 36.

$$y^{2}=\frac{-40}{36}$$

Whakahekea te hautanga \frac{-40}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$y^{2}=-\frac{10}{9}$$

Kua oti te whārite te whakatau.

$$y=\frac{\sqrt{10}i}{3} y=-\frac{\sqrt{10}i}{3}$$

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.

$$36y^{2}+40=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 36 mō a, 0 mō b, me 40 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 36\times 40}}{2\times 36}$$

Pūrua 0.

$$y=\frac{0±\sqrt{-4\times 36\times 40}}{2\times 36}$$

Whakareatia -4 ki te 36.

$$y=\frac{0±\sqrt{-144\times 40}}{2\times 36}$$

Whakareatia -144 ki te 40.

$$y=\frac{0±\sqrt{-5760}}{2\times 36}$$

Tuhia te pūtakerua o te -5760.

$$y=\frac{0±24\sqrt{10}i}{2\times 36}$$

Whakareatia 2 ki te 36.

$$y=\frac{0±24\sqrt{10}i}{72}$$

Nā, me whakaoti te whārite y=\frac{0±24\sqrt{10}i}{72} ina he tāpiri te ±.

$$y=\frac{\sqrt{10}i}{3}$$

Nā, me whakaoti te whārite y=\frac{0±24\sqrt{10}i}{72} ina he tango te ±.

$$y=-\frac{\sqrt{10}i}{3}$$

Kua oti te whārite te whakatau.

$$y=\frac{\sqrt{10}i}{3} y=-\frac{\sqrt{10}i}{3}$$