Whakaoti i te 5^14x^2-5^12=0

$$5 ^ { 14 } x ^ { 2 } - 5 ^ { 12 } = 0$$

Whakaoti mō x

$$x=\frac{1}{5}=0.2$$

$$x=-\frac{1}{5}=-0.2$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tātaihia te 5 mā te pū o 14, kia riro ko 6103515625.

$$6103515625x^{2}-5^{12}=0$$

Tātaihia te 5 mā te pū o 12, kia riro ko 244140625.

$$6103515625x^{2}-244140625=0$$

Whakawehea ngā taha e rua ki te 244140625.

$$25x^{2}-1=0$$

Whakaarohia te 25x^{2}-1. Tuhia anō te 25x^{2}-1 hei \left(5x\right)^{2}-1^{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).

$$\left(5x-1\right)\left(5x+1\right)=0$$

Hei kimi otinga whārite, me whakaoti te 5x-1=0 me te 5x+1=0.

$$x=\frac{1}{5} x=-\frac{1}{5}$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 5 mā te pū o 14, kia riro ko 6103515625.

$$6103515625x^{2}-5^{12}=0$$

Tātaihia te 5 mā te pū o 12, kia riro ko 244140625.

$$6103515625x^{2}-244140625=0$$

Me tāpiri te 244140625 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$6103515625x^{2}=244140625$$

Whakawehea ngā taha e rua ki te 6103515625.

$$x^{2}=\frac{244140625}{6103515625}$$

Whakahekea te hautanga \frac{244140625}{6103515625} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 244140625.

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

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

$$x=\frac{1}{5} x=-\frac{1}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 5 mā te pū o 14, kia riro ko 6103515625.

$$6103515625x^{2}-5^{12}=0$$

Tātaihia te 5 mā te pū o 12, kia riro ko 244140625.

$$6103515625x^{2}-244140625=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6103515625 mō a, 0 mō b, me -244140625 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6103515625\left(-244140625\right)}}{2\times 6103515625}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 6103515625\left(-244140625\right)}}{2\times 6103515625}$$

Whakareatia -4 ki te 6103515625.

$$x=\frac{0±\sqrt{-24414062500\left(-244140625\right)}}{2\times 6103515625}$$

Whakareatia -24414062500 ki te -244140625.

$$x=\frac{0±\sqrt{5960464477539062500}}{2\times 6103515625}$$

Tuhia te pūtakerua o te 5960464477539062500.

$$x=\frac{0±2441406250}{2\times 6103515625}$$

Whakareatia 2 ki te 6103515625.

$$x=\frac{0±2441406250}{12207031250}$$

Nā, me whakaoti te whārite x=\frac{0±2441406250}{12207031250} ina he tāpiri te ±. Whakahekea te hautanga \frac{2441406250}{12207031250} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2441406250.

$$x=\frac{1}{5}$$

Nā, me whakaoti te whārite x=\frac{0±2441406250}{12207031250} ina he tango te ±. Whakahekea te hautanga \frac{-2441406250}{12207031250} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2441406250.

$$x=-\frac{1}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{5} x=-\frac{1}{5}$$