Whakaoti i te 4b^2-121=0

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

Whakaoti mō b

$$b = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

$$b = -\frac{11}{2} = -5\frac{1}{2} = -5.5$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

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

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

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

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

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 121 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

Whakawehea ngā taha e rua ki te 4.

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

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

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

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.

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

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

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

Pūrua 0.

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

Whakareatia -4 ki te 4.

$$b=\frac{0±\sqrt{-16\left(-121\right)}}{2\times 4}$$

Whakareatia -16 ki te -121.

$$b=\frac{0±\sqrt{1936}}{2\times 4}$$

Tuhia te pūtakerua o te 1936.

$$b=\frac{0±44}{2\times 4}$$

Whakareatia 2 ki te 4.

$$b=\frac{0±44}{8}$$

Nā, me whakaoti te whārite b=\frac{0±44}{8} ina he tāpiri te ±. Whakahekea te hautanga \frac{44}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Nā, me whakaoti te whārite b=\frac{0±44}{8} ina he tango te ±. Whakahekea te hautanga \frac{-44}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Kua oti te whārite te whakatau.

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