Whakaoti i te 25x^2-1=0

$$25 x ^ { 2 } - 1 = 0$$

Whakaoti mō x

$$x=\frac{1}{5}=0.2$$

$$x=-\frac{1}{5}=-0.2$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakaarohia te 25x^{2}-1. Tuhia anō te 25x^{2}-1 hei \left(5x\right)^{2}-1^{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).

$$\left(5x-1\right)\left(5x+1\right)=0$$

Hei kimi otinga whārite, me whakaoti te 5x-1=0 me te 5x+1=0.

$$x=\frac{1}{5} x=-\frac{1}{5}$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 1 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$25x^{2}=1$$

Whakawehea ngā taha e rua ki te 25.

$$x^{2}=\frac{1}{25}$$

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

$$x=\frac{1}{5} x=-\frac{1}{5}$$

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.

$$25x^{2}-1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 25 mō a, 0 mō b, me -1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 25\left(-1\right)}}{2\times 25}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 25\left(-1\right)}}{2\times 25}$$

Whakareatia -4 ki te 25.

$$x=\frac{0±\sqrt{-100\left(-1\right)}}{2\times 25}$$

Whakareatia -100 ki te -1.

$$x=\frac{0±\sqrt{100}}{2\times 25}$$

Tuhia te pūtakerua o te 100.

$$x=\frac{0±10}{2\times 25}$$

Whakareatia 2 ki te 25.

$$x=\frac{0±10}{50}$$

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

$$x=\frac{1}{5}$$

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

$$x=-\frac{1}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{5} x=-\frac{1}{5}$$