Whakaoti i te 25w^2-16=0

$$25 w ^ { 2 } - 16 = 0$$

Whakaoti mō w

$$w=\frac{4}{5}=0.8$$

$$w=-\frac{4}{5}=-0.8$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakaarohia te 25w^{2}-16. Tuhia anō te 25w^{2}-16 hei \left(5w\right)^{2}-4^{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).

$$\left(5w-4\right)\left(5w+4\right)=0$$

Hei kimi otinga whārite, me whakaoti te 5w-4=0 me te 5w+4=0.

$$w=\frac{4}{5} w=-\frac{4}{5}$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 16 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$25w^{2}=16$$

Whakawehea ngā taha e rua ki te 25.

$$w^{2}=\frac{16}{25}$$

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

$$w=\frac{4}{5} w=-\frac{4}{5}$$

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.

$$25w^{2}-16=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 25 mō a, 0 mō b, me -16 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\times 25\left(-16\right)}}{2\times 25}$$

Pūrua 0.

$$w=\frac{0±\sqrt{-4\times 25\left(-16\right)}}{2\times 25}$$

Whakareatia -4 ki te 25.

$$w=\frac{0±\sqrt{-100\left(-16\right)}}{2\times 25}$$

Whakareatia -100 ki te -16.

$$w=\frac{0±\sqrt{1600}}{2\times 25}$$

Tuhia te pūtakerua o te 1600.

$$w=\frac{0±40}{2\times 25}$$

Whakareatia 2 ki te 25.

$$w=\frac{0±40}{50}$$

Nā, me whakaoti te whārite w=\frac{0±40}{50} ina he tāpiri te ±. Whakahekea te hautanga \frac{40}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$w=\frac{4}{5}$$

Nā, me whakaoti te whārite w=\frac{0±40}{50} ina he tango te ±. Whakahekea te hautanga \frac{-40}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$w=-\frac{4}{5}$$

Kua oti te whārite te whakatau.

$$w=\frac{4}{5} w=-\frac{4}{5}$$