Whakaoti i te 2x^2+left(-xright)^2=180

$$2 { x }^{ 2 } + { \left(-x \right) }^{ 2 } =180$$

Whakaoti mō x

$$x=2\sqrt{15}\approx 7.745966692$$

$$x=-2\sqrt{15}\approx -7.745966692$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te -x mā te pū o 2, kia riro ko x^{2}.

$$2x^{2}+x^{2}=180$$

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

$$3x^{2}=180$$

Whakawehea ngā taha e rua ki te 3.

$$x^{2}=\frac{180}{3}$$

Whakawehea te 180 ki te 3, kia riro ko 60.

$$x^{2}=60$$

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

$$x=2\sqrt{15} x=-2\sqrt{15}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te -x mā te pū o 2, kia riro ko x^{2}.

$$2x^{2}+x^{2}=180$$

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

$$3x^{2}=180$$

Tangohia te 180 mai i ngā taha e rua.

$$3x^{2}-180=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me -180 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-180\right)}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-180\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\left(-180\right)}}{2\times 3}$$

Whakareatia -12 ki te -180.

$$x=\frac{0±\sqrt{2160}}{2\times 3}$$

Tuhia te pūtakerua o te 2160.

$$x=\frac{0±12\sqrt{15}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±12\sqrt{15}}{6}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{15}}{6} ina he tāpiri te ±.

$$x=2\sqrt{15}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{15}}{6} ina he tango te ±.

$$x=-2\sqrt{15}$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{15} x=-2\sqrt{15}$$