Whakaoti i te 588=4*10*h^2/48

$$588 = \frac { 4 \times 10 \times h ^ { 2 } } { 48 }$$

Whakaoti mō h

$$h = \frac{42 \sqrt{10}}{5} \approx 26.563132345$$

$$h = -\frac{42 \sqrt{10}}{5} \approx -26.563132345$$

Ngā Upane mā te Kimi Pūtakerua

Me whakarea ngā taha e rua ki te 48.

$$588\times 48=4\times 10h^{2}$$

Whakareatia te 588 ki te 48, ka 28224.

$$28224=4\times 10h^{2}$$

Whakareatia te 4 ki te 10, ka 40.

$$28224=40h^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$40h^{2}=28224$$

Whakawehea ngā taha e rua ki te 40.

$$h^{2}=\frac{28224}{40}$$

Whakahekea te hautanga \frac{28224}{40} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$h^{2}=\frac{3528}{5}$$

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

$$h=\frac{42\sqrt{10}}{5} h=-\frac{42\sqrt{10}}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua ki te 48.

$$588\times 48=4\times 10h^{2}$$

Whakareatia te 588 ki te 48, ka 28224.

$$28224=4\times 10h^{2}$$

Whakareatia te 4 ki te 10, ka 40.

$$28224=40h^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$40h^{2}=28224$$

Tangohia te 28224 mai i ngā taha e rua.

$$40h^{2}-28224=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 40 mō a, 0 mō b, me -28224 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{0±\sqrt{0^{2}-4\times 40\left(-28224\right)}}{2\times 40}$$

Pūrua 0.

$$h=\frac{0±\sqrt{-4\times 40\left(-28224\right)}}{2\times 40}$$

Whakareatia -4 ki te 40.

$$h=\frac{0±\sqrt{-160\left(-28224\right)}}{2\times 40}$$

Whakareatia -160 ki te -28224.

$$h=\frac{0±\sqrt{4515840}}{2\times 40}$$

Tuhia te pūtakerua o te 4515840.

$$h=\frac{0±672\sqrt{10}}{2\times 40}$$

Whakareatia 2 ki te 40.

$$h=\frac{0±672\sqrt{10}}{80}$$

Nā, me whakaoti te whārite h=\frac{0±672\sqrt{10}}{80} ina he tāpiri te ±.

$$h=\frac{42\sqrt{10}}{5}$$

Nā, me whakaoti te whārite h=\frac{0±672\sqrt{10}}{80} ina he tango te ±.

$$h=-\frac{42\sqrt{10}}{5}$$

Kua oti te whārite te whakatau.

$$h=\frac{42\sqrt{10}}{5} h=-\frac{42\sqrt{10}}{5}$$