Whakaoti i te 10^2=2x^2+x^2

$$10 ^ { 2 } = 2 x ^ { 2 } + x ^ { 2 }$$

Whakaoti mō x

$$x = \frac{10 \sqrt{3}}{3} \approx 5.773502692$$

$$x = -\frac{10 \sqrt{3}}{3} \approx -5.773502692$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 10 mā te pū o 2, kia riro ko 100.

$$100=2x^{2}+x^{2}$$

Pahekotia te 2x^{2} me x^{2}, ka 3x^{2}.

$$100=3x^{2}$$

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

$$3x^{2}=100$$

Whakawehea ngā taha e rua ki te 3.

$$x^{2}=\frac{100}{3}$$

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

$$x=\frac{10\sqrt{3}}{3} x=-\frac{10\sqrt{3}}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 10 mā te pū o 2, kia riro ko 100.

$$100=2x^{2}+x^{2}$$

Pahekotia te 2x^{2} me x^{2}, ka 3x^{2}.

$$100=3x^{2}$$

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

$$3x^{2}=100$$

Tangohia te 100 mai i ngā taha e rua.

$$3x^{2}-100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me -100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-100\right)}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-100\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\left(-100\right)}}{2\times 3}$$

Whakareatia -12 ki te -100.

$$x=\frac{0±\sqrt{1200}}{2\times 3}$$

Tuhia te pūtakerua o te 1200.

$$x=\frac{0±20\sqrt{3}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±20\sqrt{3}}{6}$$

Nā, me whakaoti te whārite x=\frac{0±20\sqrt{3}}{6} ina he tāpiri te ±.

$$x=\frac{10\sqrt{3}}{3}$$

Nā, me whakaoti te whārite x=\frac{0±20\sqrt{3}}{6} ina he tango te ±.

$$x=-\frac{10\sqrt{3}}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{10\sqrt{3}}{3} x=-\frac{10\sqrt{3}}{3}$$