Whakaoti i te x^2+x^2-13=130

$${ x }^{ 2 } + { x }^{ 2 } -13=130$$

Whakaoti mō x

$$x = \frac{\sqrt{286}}{2} \approx 8.455767263$$

$$x = -\frac{\sqrt{286}}{2} \approx -8.455767263$$

Ngā Upane mā te Kimi Pūtakerua

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

$$2x^{2}-13=130$$

Me tāpiri te 13 ki ngā taha e rua.

$$2x^{2}=130+13$$

Tāpirihia te 130 ki te 13, ka 143.

$$2x^{2}=143$$

Whakawehea ngā taha e rua ki te 2.

$$x^{2}=\frac{143}{2}$$

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

$$x=\frac{\sqrt{286}}{2} x=-\frac{\sqrt{286}}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$2x^{2}-13=130$$

Tangohia te 130 mai i ngā taha e rua.

$$2x^{2}-13-130=0$$

Tangohia te 130 i te -13, ka -143.

$$2x^{2}-143=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me -143 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-143\right)}}{2\times 2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-143\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\left(-143\right)}}{2\times 2}$$

Whakareatia -8 ki te -143.

$$x=\frac{0±\sqrt{1144}}{2\times 2}$$

Tuhia te pūtakerua o te 1144.

$$x=\frac{0±2\sqrt{286}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±2\sqrt{286}}{4}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{286}}{4} ina he tāpiri te ±.

$$x=\frac{\sqrt{286}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{286}}{4} ina he tango te ±.

$$x=-\frac{\sqrt{286}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{286}}{2} x=-\frac{\sqrt{286}}{2}$$