Whakaoti i te 25/4x^2-1=0

$$\frac { 25 } { 4 } x ^ { 2 } - 1 = 0$$

Whakaoti mō x

$$x=\frac{2}{5}=0.4$$

$$x=-\frac{2}{5}=-0.4$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Me whakarea ngā taha e rua ki te 4.

$$25x^{2}-4=0$$

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

$$\left(5x-2\right)\left(5x+2\right)=0$$

Hei kimi otinga whārite, me whakaoti te 5x-2=0 me te 5x+2=0.

$$x=\frac{2}{5} x=-\frac{2}{5}$$

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.

$$\frac{25}{4}x^{2}=1$$

Me whakarea ngā taha e rua ki te \frac{4}{25}, te tau utu o \frac{25}{4}.

$$x^{2}=1\times \frac{4}{25}$$

Whakareatia te 1 ki te \frac{4}{25}, ka \frac{4}{25}.

$$x^{2}=\frac{4}{25}$$

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

$$x=\frac{2}{5} x=-\frac{2}{5}$$

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.

$$\frac{25}{4}x^{2}-1=0$$

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

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

Pūrua 0.

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

Whakareatia -4 ki te \frac{25}{4}.

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

Whakareatia -25 ki te -1.

$$x=\frac{0±\sqrt{25}}{2\times \frac{25}{4}}$$

Tuhia te pūtakerua o te 25.

$$x=\frac{0±5}{2\times \frac{25}{4}}$$

Whakareatia 2 ki te \frac{25}{4}.

$$x=\frac{0±5}{\frac{25}{2}}$$

Nā, me whakaoti te whārite x=\frac{0±5}{\frac{25}{2}} ina he tāpiri te ±. Whakawehe 5 ki te \frac{25}{2} mā te whakarea 5 ki te tau huripoki o \frac{25}{2}.

$$x=\frac{2}{5}$$

Nā, me whakaoti te whārite x=\frac{0±5}{\frac{25}{2}} ina he tango te ±. Whakawehe -5 ki te \frac{25}{2} mā te whakarea -5 ki te tau huripoki o \frac{25}{2}.

$$x=-\frac{2}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{2}{5} x=-\frac{2}{5}$$