Whakaoti i te 3/4+y^2=1

$$\frac { 3 } { 4 } + y ^ { 2 } = 1$$

Whakaoti mō y

$$y=\frac{1}{2}=0.5$$

$$y=-\frac{1}{2}=-0.5$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tangohia te 1 mai i ngā taha e rua.

$$\frac{3}{4}+y^{2}-1=0$$

Tangohia te 1 i te \frac{3}{4}, ka -\frac{1}{4}.

$$-\frac{1}{4}+y^{2}=0$$

Me whakarea ngā taha e rua ki te 4.

$$-1+4y^{2}=0$$

Whakaarohia te -1+4y^{2}. Tuhia anō te -1+4y^{2} hei \left(2y\right)^{2}-1^{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).

$$\left(2y-1\right)\left(2y+1\right)=0$$

Hei kimi otinga whārite, me whakaoti te 2y-1=0 me te 2y+1=0.

$$y=\frac{1}{2} y=-\frac{1}{2}$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te \frac{3}{4} mai i ngā taha e rua.

$$y^{2}=1-\frac{3}{4}$$

Tangohia te \frac{3}{4} i te 1, ka \frac{1}{4}.

$$y^{2}=\frac{1}{4}$$

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

$$y=\frac{1}{2} y=-\frac{1}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 1 mai i ngā taha e rua.

$$\frac{3}{4}+y^{2}-1=0$$

Tangohia te 1 i te \frac{3}{4}, ka -\frac{1}{4}.

$$-\frac{1}{4}+y^{2}=0$$

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.

$$y^{2}-\frac{1}{4}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -\frac{1}{4} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{4}\right)}}{2}$$

Pūrua 0.

$$y=\frac{0±\sqrt{-4\left(-\frac{1}{4}\right)}}{2}$$

Whakareatia -4 ki te -\frac{1}{4}.

$$y=\frac{0±\sqrt{1}}{2}$$

Tuhia te pūtakerua o te 1.

$$y=\frac{0±1}{2}$$

Nā, me whakaoti te whārite y=\frac{0±1}{2} ina he tāpiri te ±. Whakawehe 1 ki te 2.

$$y=\frac{1}{2}$$

Nā, me whakaoti te whārite y=\frac{0±1}{2} ina he tango te ±. Whakawehe -1 ki te 2.

$$y=-\frac{1}{2}$$

Kua oti te whārite te whakatau.

$$y=\frac{1}{2} y=-\frac{1}{2}$$