Whakaoti i te 16k^2-144=0

$$16 k ^ { 2 } - 144 = 0$$

Whakaoti mō k

$$k=3$$

$$k=-3$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te 16.

$$k^{2}-9=0$$

Whakaarohia te k^{2}-9. Tuhia anō te k^{2}-9 hei k^{2}-3^{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).

$$\left(k-3\right)\left(k+3\right)=0$$

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

$$k=3 k=-3$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 144 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$16k^{2}=144$$

Whakawehea ngā taha e rua ki te 16.

$$k^{2}=\frac{144}{16}$$

Whakawehea te 144 ki te 16, kia riro ko 9.

$$k^{2}=9$$

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

$$k=3 k=-3$$

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.

$$16k^{2}-144=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 16 mō a, 0 mō b, me -144 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\times 16\left(-144\right)}}{2\times 16}$$

Pūrua 0.

$$k=\frac{0±\sqrt{-4\times 16\left(-144\right)}}{2\times 16}$$

Whakareatia -4 ki te 16.

$$k=\frac{0±\sqrt{-64\left(-144\right)}}{2\times 16}$$

Whakareatia -64 ki te -144.

$$k=\frac{0±\sqrt{9216}}{2\times 16}$$

Tuhia te pūtakerua o te 9216.

$$k=\frac{0±96}{2\times 16}$$

Whakareatia 2 ki te 16.

$$k=\frac{0±96}{32}$$

Nā, me whakaoti te whārite k=\frac{0±96}{32} ina he tāpiri te ±. Whakawehe 96 ki te 32.

$$k=3$$

Nā, me whakaoti te whārite k=\frac{0±96}{32} ina he tango te ±. Whakawehe -96 ki te 32.

$$k=-3$$

Kua oti te whārite te whakatau.

$$k=3 k=-3$$