Whakaoti i te 9p^2=49

$$9 p ^ { 2 } = 49$$

Whakaoti mō p

$$p = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

$$p = -\frac{7}{3} = -2\frac{1}{3} \approx -2.333333333$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te 9.

$$p^{2}=\frac{49}{9}$$

Tangohia te \frac{49}{9} mai i ngā taha e rua.

$$p^{2}-\frac{49}{9}=0$$

Me whakarea ngā taha e rua ki te 9.

$$9p^{2}-49=0$$

Whakaarohia te 9p^{2}-49. Tuhia anō te 9p^{2}-49 hei \left(3p\right)^{2}-7^{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).

$$\left(3p-7\right)\left(3p+7\right)=0$$

Hei kimi otinga whārite, me whakaoti te 3p-7=0 me te 3p+7=0.

$$p=\frac{7}{3} p=-\frac{7}{3}$$

Ngā Upane mā te Kimi Pūtakerua

Whakawehea ngā taha e rua ki te 9.

$$p^{2}=\frac{49}{9}$$

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

$$p=\frac{7}{3} p=-\frac{7}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ngā taha e rua ki te 9.

$$p^{2}=\frac{49}{9}$$

Tangohia te \frac{49}{9} mai i ngā taha e rua.

$$p^{2}-\frac{49}{9}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -\frac{49}{9} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\left(-\frac{49}{9}\right)}}{2}$$

Pūrua 0.

$$p=\frac{0±\sqrt{-4\left(-\frac{49}{9}\right)}}{2}$$

Whakareatia -4 ki te -\frac{49}{9}.

$$p=\frac{0±\sqrt{\frac{196}{9}}}{2}$$

Tuhia te pūtakerua o te \frac{196}{9}.

$$p=\frac{0±\frac{14}{3}}{2}$$

Nā, me whakaoti te whārite p=\frac{0±\frac{14}{3}}{2} ina he tāpiri te ±.

$$p=\frac{7}{3}$$

Nā, me whakaoti te whārite p=\frac{0±\frac{14}{3}}{2} ina he tango te ±.

$$p=-\frac{7}{3}$$

Kua oti te whārite te whakatau.

$$p=\frac{7}{3} p=-\frac{7}{3}$$