Whakaoti i te 4p^2-7=13

$$4 p ^ { 2 } - 7 = 13$$

Whakaoti mō p

$$p=\sqrt{5}\approx 2.236067977$$

$$p=-\sqrt{5}\approx -2.236067977$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 7 ki ngā taha e rua.

$$4p^{2}=13+7$$

Tāpirihia te 13 ki te 7, ka 20.

$$4p^{2}=20$$

Whakawehea ngā taha e rua ki te 4.

$$p^{2}=\frac{20}{4}$$

Whakawehea te 20 ki te 4, kia riro ko 5.

$$p^{2}=5$$

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

$$p=\sqrt{5} p=-\sqrt{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 13 mai i ngā taha e rua.

$$4p^{2}-7-13=0$$

Tangohia te 13 i te -7, ka -20.

$$4p^{2}-20=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 0 mō b, me -20 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\times 4\left(-20\right)}}{2\times 4}$$

Pūrua 0.

$$p=\frac{0±\sqrt{-4\times 4\left(-20\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$p=\frac{0±\sqrt{-16\left(-20\right)}}{2\times 4}$$

Whakareatia -16 ki te -20.

$$p=\frac{0±\sqrt{320}}{2\times 4}$$

Tuhia te pūtakerua o te 320.

$$p=\frac{0±8\sqrt{5}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$p=\frac{0±8\sqrt{5}}{8}$$

Nā, me whakaoti te whārite p=\frac{0±8\sqrt{5}}{8} ina he tāpiri te ±.

$$p=\sqrt{5}$$

Nā, me whakaoti te whārite p=\frac{0±8\sqrt{5}}{8} ina he tango te ±.

$$p=-\sqrt{5}$$

Kua oti te whārite te whakatau.

$$p=\sqrt{5} p=-\sqrt{5}$$