Whakaoti i te eta_g^2=5^2+12^2

$$\eta _ { g } ^ { 2 } = 5 ^ { 2 } + 12 ^ { 2 }$$

Whakaoti mō η_g

$$\eta _{g}=-13$$

$$\eta _{g}=13$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$\eta _{g}^{2}=25+12^{2}$$

Tātaihia te 12 mā te pū o 2, kia riro ko 144.

$$\eta _{g}^{2}=25+144$$

Tāpirihia te 25 ki te 144, ka 169.

$$\eta _{g}^{2}=169$$

Tangohia te 169 mai i ngā taha e rua.

$$\eta _{g}^{2}-169=0$$

Whakaarohia te \eta _{g}^{2}-169. Tuhia anō te \eta _{g}^{2}-169 hei \eta _{g}^{2}-13^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(\eta _{g}-13\right)\left(\eta _{g}+13\right)=0$$

Hei kimi otinga whārite, me whakaoti te \eta _{g}-13=0 me te \eta _{g}+13=0.

$$\eta _{g}=13 \eta _{g}=-13$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$\eta _{g}^{2}=25+12^{2}$$

Tātaihia te 12 mā te pū o 2, kia riro ko 144.

$$\eta _{g}^{2}=25+144$$

Tāpirihia te 25 ki te 144, ka 169.

$$\eta _{g}^{2}=169$$

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

$$\eta _{g}=13 \eta _{g}=-13$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$\eta _{g}^{2}=25+12^{2}$$

Tātaihia te 12 mā te pū o 2, kia riro ko 144.

$$\eta _{g}^{2}=25+144$$

Tāpirihia te 25 ki te 144, ka 169.

$$\eta _{g}^{2}=169$$

Tangohia te 169 mai i ngā taha e rua.

$$\eta _{g}^{2}-169=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -169 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\eta _{g}=\frac{0±\sqrt{0^{2}-4\left(-169\right)}}{2}$$

Pūrua 0.

$$\eta _{g}=\frac{0±\sqrt{-4\left(-169\right)}}{2}$$

Whakareatia -4 ki te -169.

$$\eta _{g}=\frac{0±\sqrt{676}}{2}$$

Tuhia te pūtakerua o te 676.

$$\eta _{g}=\frac{0±26}{2}$$

Nā, me whakaoti te whārite \eta _{g}=\frac{0±26}{2} ina he tāpiri te ±. Whakawehe 26 ki te 2.

$$\eta _{g}=13$$

Nā, me whakaoti te whārite \eta _{g}=\frac{0±26}{2} ina he tango te ±. Whakawehe -26 ki te 2.

$$\eta _{g}=-13$$

Kua oti te whārite te whakatau.

$$\eta _{g}=13 \eta _{g}=-13$$