Whakaoti i te 121h^2-4=0

$$121 h ^ { 2 } - 4 = 0$$

Whakaoti mō h

$$h=\frac{2}{11}\approx 0.181818182$$

$$h=-\frac{2}{11}\approx -0.181818182$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakaarohia te 121h^{2}-4. Tuhia anō te 121h^{2}-4 hei \left(11h\right)^{2}-2^{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).

$$\left(11h-2\right)\left(11h+2\right)=0$$

Hei kimi otinga whārite, me whakaoti te 11h-2=0 me te 11h+2=0.

$$h=\frac{2}{11} h=-\frac{2}{11}$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 4 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$121h^{2}=4$$

Whakawehea ngā taha e rua ki te 121.

$$h^{2}=\frac{4}{121}$$

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

$$h=\frac{2}{11} h=-\frac{2}{11}$$

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.

$$121h^{2}-4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 121 mō a, 0 mō b, me -4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{0±\sqrt{0^{2}-4\times 121\left(-4\right)}}{2\times 121}$$

Pūrua 0.

$$h=\frac{0±\sqrt{-4\times 121\left(-4\right)}}{2\times 121}$$

Whakareatia -4 ki te 121.

$$h=\frac{0±\sqrt{-484\left(-4\right)}}{2\times 121}$$

Whakareatia -484 ki te -4.

$$h=\frac{0±\sqrt{1936}}{2\times 121}$$

Tuhia te pūtakerua o te 1936.

$$h=\frac{0±44}{2\times 121}$$

Whakareatia 2 ki te 121.

$$h=\frac{0±44}{242}$$

Nā, me whakaoti te whārite h=\frac{0±44}{242} ina he tāpiri te ±. Whakahekea te hautanga \frac{44}{242} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 22.

$$h=\frac{2}{11}$$

Nā, me whakaoti te whārite h=\frac{0±44}{242} ina he tango te ±. Whakahekea te hautanga \frac{-44}{242} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 22.

$$h=-\frac{2}{11}$$

Kua oti te whārite te whakatau.

$$h=\frac{2}{11} h=-\frac{2}{11}$$