Whakaoti i te 49b^2-9=0

$$49 b ^ { 2 } - 9 = 0$$

Whakaoti mō b

$$b=\frac{3}{7}\approx 0.428571429$$

$$b=-\frac{3}{7}\approx -0.428571429$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakaarohia te 49b^{2}-9. Tuhia anō te 49b^{2}-9 hei \left(7b\right)^{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).

$$\left(7b-3\right)\left(7b+3\right)=0$$

Hei kimi otinga whārite, me whakaoti te 7b-3=0 me te 7b+3=0.

$$b=\frac{3}{7} b=-\frac{3}{7}$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 9 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$49b^{2}=9$$

Whakawehea ngā taha e rua ki te 49.

$$b^{2}=\frac{9}{49}$$

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

$$b=\frac{3}{7} b=-\frac{3}{7}$$

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.

$$49b^{2}-9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 49 mō a, 0 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 49\left(-9\right)}}{2\times 49}$$

Pūrua 0.

$$b=\frac{0±\sqrt{-4\times 49\left(-9\right)}}{2\times 49}$$

Whakareatia -4 ki te 49.

$$b=\frac{0±\sqrt{-196\left(-9\right)}}{2\times 49}$$

Whakareatia -196 ki te -9.

$$b=\frac{0±\sqrt{1764}}{2\times 49}$$

Tuhia te pūtakerua o te 1764.

$$b=\frac{0±42}{2\times 49}$$

Whakareatia 2 ki te 49.

$$b=\frac{0±42}{98}$$

Nā, me whakaoti te whārite b=\frac{0±42}{98} ina he tāpiri te ±. Whakahekea te hautanga \frac{42}{98} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

$$b=\frac{3}{7}$$

Nā, me whakaoti te whārite b=\frac{0±42}{98} ina he tango te ±. Whakahekea te hautanga \frac{-42}{98} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

$$b=-\frac{3}{7}$$

Kua oti te whārite te whakatau.

$$b=\frac{3}{7} b=-\frac{3}{7}$$