Whakaoti i te 10*10=b^2*2

$$10 \times 10 = b ^ { 2 } \times 2$$

Whakaoti mō b

$$b=5\sqrt{2}\approx 7.071067812$$

$$b=-5\sqrt{2}\approx -7.071067812$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te 10 ki te 10, ka 100.

$$100=b^{2}\times 2$$

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

$$b^{2}\times 2=100$$

Whakawehea ngā taha e rua ki te 2.

$$b^{2}=\frac{100}{2}$$

Whakawehea te 100 ki te 2, kia riro ko 50.

$$b^{2}=50$$

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

$$b=5\sqrt{2} b=-5\sqrt{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 10 ki te 10, ka 100.

$$100=b^{2}\times 2$$

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

$$b^{2}\times 2=100$$

Tangohia te 100 mai i ngā taha e rua.

$$b^{2}\times 2-100=0$$

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.

$$2b^{2}-100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me -100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 2\left(-100\right)}}{2\times 2}$$

Pūrua 0.

$$b=\frac{0±\sqrt{-4\times 2\left(-100\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$b=\frac{0±\sqrt{-8\left(-100\right)}}{2\times 2}$$

Whakareatia -8 ki te -100.

$$b=\frac{0±\sqrt{800}}{2\times 2}$$

Tuhia te pūtakerua o te 800.

$$b=\frac{0±20\sqrt{2}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$b=\frac{0±20\sqrt{2}}{4}$$

Nā, me whakaoti te whārite b=\frac{0±20\sqrt{2}}{4} ina he tāpiri te ±.

$$b=5\sqrt{2}$$

Nā, me whakaoti te whārite b=\frac{0±20\sqrt{2}}{4} ina he tango te ±.

$$b=-5\sqrt{2}$$

Kua oti te whārite te whakatau.

$$b=5\sqrt{2} b=-5\sqrt{2}$$