Whakaoti i te 16/4-9/b^2=1

$$\frac { 16 } { 4 } - \frac { 9 } { b ^ { 2 } } = 1$$

Whakaoti mō b

$$b=\sqrt{3}\approx 1.732050808$$

$$b=-\sqrt{3}\approx -1.732050808$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe b ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 4b^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o 4,b^{2}.

$$b^{2}\times 16-4\times 9=4b^{2}$$

Whakareatia te -4 ki te 9, ka -36.

$$b^{2}\times 16-36=4b^{2}$$

Tangohia te 4b^{2} mai i ngā taha e rua.

$$b^{2}\times 16-36-4b^{2}=0$$

Pahekotia te b^{2}\times 16 me -4b^{2}, ka 12b^{2}.

$$12b^{2}-36=0$$

Me tāpiri te 36 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$12b^{2}=36$$

Whakawehea ngā taha e rua ki te 12.

$$b^{2}=\frac{36}{12}$$

Whakawehea te 36 ki te 12, kia riro ko 3.

$$b^{2}=3$$

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

$$b=\sqrt{3} b=-\sqrt{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe b ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 4b^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o 4,b^{2}.

$$b^{2}\times 16-4\times 9=4b^{2}$$

Whakareatia te -4 ki te 9, ka -36.

$$b^{2}\times 16-36=4b^{2}$$

Tangohia te 4b^{2} mai i ngā taha e rua.

$$b^{2}\times 16-36-4b^{2}=0$$

Pahekotia te b^{2}\times 16 me -4b^{2}, ka 12b^{2}.

$$12b^{2}-36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 12 mō a, 0 mō b, me -36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 12\left(-36\right)}}{2\times 12}$$

Pūrua 0.

$$b=\frac{0±\sqrt{-4\times 12\left(-36\right)}}{2\times 12}$$

Whakareatia -4 ki te 12.

$$b=\frac{0±\sqrt{-48\left(-36\right)}}{2\times 12}$$

Whakareatia -48 ki te -36.

$$b=\frac{0±\sqrt{1728}}{2\times 12}$$

Tuhia te pūtakerua o te 1728.

$$b=\frac{0±24\sqrt{3}}{2\times 12}$$

Whakareatia 2 ki te 12.

$$b=\frac{0±24\sqrt{3}}{24}$$

Nā, me whakaoti te whārite b=\frac{0±24\sqrt{3}}{24} ina he tāpiri te ±.

$$b=\sqrt{3}$$

Nā, me whakaoti te whārite b=\frac{0±24\sqrt{3}}{24} ina he tango te ±.

$$b=-\sqrt{3}$$

Kua oti te whārite te whakatau.

$$b=\sqrt{3} b=-\sqrt{3}$$