Whakaoti i te 4r^2-81=0

$$4 r ^ { 2 } - 81 = 0$$

Whakaoti mō r

$$r = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

$$r = -\frac{9}{2} = -4\frac{1}{2} = -4.5$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakaarohia te 4r^{2}-81. Tuhia anō te 4r^{2}-81 hei \left(2r\right)^{2}-9^{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).

$$\left(2r-9\right)\left(2r+9\right)=0$$

Hei kimi otinga whārite, me whakaoti te 2r-9=0 me te 2r+9=0.

$$r=\frac{9}{2} r=-\frac{9}{2}$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 81 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$4r^{2}=81$$

Whakawehea ngā taha e rua ki te 4.

$$r^{2}=\frac{81}{4}$$

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

$$r=\frac{9}{2} r=-\frac{9}{2}$$

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.

$$4r^{2}-81=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 0 mō b, me -81 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 4\left(-81\right)}}{2\times 4}$$

Pūrua 0.

$$r=\frac{0±\sqrt{-4\times 4\left(-81\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$r=\frac{0±\sqrt{-16\left(-81\right)}}{2\times 4}$$

Whakareatia -16 ki te -81.

$$r=\frac{0±\sqrt{1296}}{2\times 4}$$

Tuhia te pūtakerua o te 1296.

$$r=\frac{0±36}{2\times 4}$$

Whakareatia 2 ki te 4.

$$r=\frac{0±36}{8}$$

Nā, me whakaoti te whārite r=\frac{0±36}{8} ina he tāpiri te ±. Whakahekea te hautanga \frac{36}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$r=\frac{9}{2}$$

Nā, me whakaoti te whārite r=\frac{0±36}{8} ina he tango te ±. Whakahekea te hautanga \frac{-36}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$r=-\frac{9}{2}$$

Kua oti te whārite te whakatau.

$$r=\frac{9}{2} r=-\frac{9}{2}$$