Whakaoti i te 16b^2-25=0

$$16 b ^ { 2 } - 25 = 0$$

Whakaoti mō b

$$b = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

$$b = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakaarohia te 16b^{2}-25. Tuhia anō te 16b^{2}-25 hei \left(4b\right)^{2}-5^{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).

$$\left(4b-5\right)\left(4b+5\right)=0$$

Hei kimi otinga whārite, me whakaoti te 4b-5=0 me te 4b+5=0.

$$b=\frac{5}{4} b=-\frac{5}{4}$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 25 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$16b^{2}=25$$

Whakawehea ngā taha e rua ki te 16.

$$b^{2}=\frac{25}{16}$$

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

$$b=\frac{5}{4} b=-\frac{5}{4}$$

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.

$$16b^{2}-25=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 16 mō a, 0 mō b, me -25 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 16\left(-25\right)}}{2\times 16}$$

Pūrua 0.

$$b=\frac{0±\sqrt{-4\times 16\left(-25\right)}}{2\times 16}$$

Whakareatia -4 ki te 16.

$$b=\frac{0±\sqrt{-64\left(-25\right)}}{2\times 16}$$

Whakareatia -64 ki te -25.

$$b=\frac{0±\sqrt{1600}}{2\times 16}$$

Tuhia te pūtakerua o te 1600.

$$b=\frac{0±40}{2\times 16}$$

Whakareatia 2 ki te 16.

$$b=\frac{0±40}{32}$$

Nā, me whakaoti te whārite b=\frac{0±40}{32} ina he tāpiri te ±. Whakahekea te hautanga \frac{40}{32} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$b=\frac{5}{4}$$

Nā, me whakaoti te whārite b=\frac{0±40}{32} ina he tango te ±. Whakahekea te hautanga \frac{-40}{32} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$b=-\frac{5}{4}$$

Kua oti te whārite te whakatau.

$$b=\frac{5}{4} b=-\frac{5}{4}$$