Whakaoti i te 5y^2+1=8

$$5 y ^ { 2 } + 1 = 8$$

Whakaoti mō y

$$y = \frac{\sqrt{35}}{5} \approx 1.183215957$$

$$y = -\frac{\sqrt{35}}{5} \approx -1.183215957$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 1 mai i ngā taha e rua.

$$5y^{2}=8-1$$

Tangohia te 1 i te 8, ka 7.

$$5y^{2}=7$$

Whakawehea ngā taha e rua ki te 5.

$$y^{2}=\frac{7}{5}$$

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

$$y=\frac{\sqrt{35}}{5} y=-\frac{\sqrt{35}}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 8 mai i ngā taha e rua.

$$5y^{2}+1-8=0$$

Tangohia te 8 i te 1, ka -7.

$$5y^{2}-7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 0 mō b, me -7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 5\left(-7\right)}}{2\times 5}$$

Pūrua 0.

$$y=\frac{0±\sqrt{-4\times 5\left(-7\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$y=\frac{0±\sqrt{-20\left(-7\right)}}{2\times 5}$$

Whakareatia -20 ki te -7.

$$y=\frac{0±\sqrt{140}}{2\times 5}$$

Tuhia te pūtakerua o te 140.

$$y=\frac{0±2\sqrt{35}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$y=\frac{0±2\sqrt{35}}{10}$$

Nā, me whakaoti te whārite y=\frac{0±2\sqrt{35}}{10} ina he tāpiri te ±.

$$y=\frac{\sqrt{35}}{5}$$

Nā, me whakaoti te whārite y=\frac{0±2\sqrt{35}}{10} ina he tango te ±.

$$y=-\frac{\sqrt{35}}{5}$$

Kua oti te whārite te whakatau.

$$y=\frac{\sqrt{35}}{5} y=-\frac{\sqrt{35}}{5}$$