Whakaoti i te 144q^2=25

$$144 q ^ { 2 } = 25$$

Whakaoti mō q

$$q=\frac{5}{12}\approx 0.416666667$$

$$q=-\frac{5}{12}\approx -0.416666667$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te 144.

$$q^{2}=\frac{25}{144}$$

Tangohia te \frac{25}{144} mai i ngā taha e rua.

$$q^{2}-\frac{25}{144}=0$$

Me whakarea ngā taha e rua ki te 144.

$$144q^{2}-25=0$$

Whakaarohia te 144q^{2}-25. Tuhia anō te 144q^{2}-25 hei \left(12q\right)^{2}-5^{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).

$$\left(12q-5\right)\left(12q+5\right)=0$$

Hei kimi otinga whārite, me whakaoti te 12q-5=0 me te 12q+5=0.

$$q=\frac{5}{12} q=-\frac{5}{12}$$

Ngā Upane mā te Kimi Pūtakerua

Whakawehea ngā taha e rua ki te 144.

$$q^{2}=\frac{25}{144}$$

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

$$q=\frac{5}{12} q=-\frac{5}{12}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ngā taha e rua ki te 144.

$$q^{2}=\frac{25}{144}$$

Tangohia te \frac{25}{144} mai i ngā taha e rua.

$$q^{2}-\frac{25}{144}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -\frac{25}{144} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{0±\sqrt{0^{2}-4\left(-\frac{25}{144}\right)}}{2}$$

Pūrua 0.

$$q=\frac{0±\sqrt{-4\left(-\frac{25}{144}\right)}}{2}$$

Whakareatia -4 ki te -\frac{25}{144}.

$$q=\frac{0±\sqrt{\frac{25}{36}}}{2}$$

Tuhia te pūtakerua o te \frac{25}{36}.

$$q=\frac{0±\frac{5}{6}}{2}$$

Nā, me whakaoti te whārite q=\frac{0±\frac{5}{6}}{2} ina he tāpiri te ±.

$$q=\frac{5}{12}$$

Nā, me whakaoti te whārite q=\frac{0±\frac{5}{6}}{2} ina he tango te ±.

$$q=-\frac{5}{12}$$

Kua oti te whārite te whakatau.

$$q=\frac{5}{12} q=-\frac{5}{12}$$