Whakaoti i te (3sqrt{17})^2+4^2=h^2

$$( 3 \sqrt { 17 } ) ^ { 2 } + 4 ^ { 2 } = h ^ { 2 }$$

Whakaoti mō h

$$h=13$$

$$h=-13$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakarohaina te \left(3\sqrt{17}\right)^{2}.

$$3^{2}\left(\sqrt{17}\right)^{2}+4^{2}=h^{2}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$9\left(\sqrt{17}\right)^{2}+4^{2}=h^{2}$$

Ko te pūrua o \sqrt{17} ko 17.

$$9\times 17+4^{2}=h^{2}$$

Whakareatia te 9 ki te 17, ka 153.

$$153+4^{2}=h^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$153+16=h^{2}$$

Tāpirihia te 153 ki te 16, ka 169.

$$169=h^{2}$$

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

$$h^{2}=169$$

Tangohia te 169 mai i ngā taha e rua.

$$h^{2}-169=0$$

Whakaarohia te h^{2}-169. Tuhia anō te h^{2}-169 hei h^{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).

$$\left(h-13\right)\left(h+13\right)=0$$

Hei kimi otinga whārite, me whakaoti te h-13=0 me te h+13=0.

$$h=13 h=-13$$

Ngā Upane mā te Kimi Pūtakerua

Whakarohaina te \left(3\sqrt{17}\right)^{2}.

$$3^{2}\left(\sqrt{17}\right)^{2}+4^{2}=h^{2}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$9\left(\sqrt{17}\right)^{2}+4^{2}=h^{2}$$

Ko te pūrua o \sqrt{17} ko 17.

$$9\times 17+4^{2}=h^{2}$$

Whakareatia te 9 ki te 17, ka 153.

$$153+4^{2}=h^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$153+16=h^{2}$$

Tāpirihia te 153 ki te 16, ka 169.

$$169=h^{2}$$

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

$$h^{2}=169$$

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

$$h=13 h=-13$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakarohaina te \left(3\sqrt{17}\right)^{2}.

$$3^{2}\left(\sqrt{17}\right)^{2}+4^{2}=h^{2}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$9\left(\sqrt{17}\right)^{2}+4^{2}=h^{2}$$

Ko te pūrua o \sqrt{17} ko 17.

$$9\times 17+4^{2}=h^{2}$$

Whakareatia te 9 ki te 17, ka 153.

$$153+4^{2}=h^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$153+16=h^{2}$$

Tāpirihia te 153 ki te 16, ka 169.

$$169=h^{2}$$

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

$$h^{2}=169$$

Tangohia te 169 mai i ngā taha e rua.

$$h^{2}-169=0$$

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}.

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

Pūrua 0.

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

Whakareatia -4 ki te -169.

$$h=\frac{0±\sqrt{676}}{2}$$

Tuhia te pūtakerua o te 676.

$$h=\frac{0±26}{2}$$

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

$$h=13$$

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

$$h=-13$$

Kua oti te whārite te whakatau.

$$h=13 h=-13$$