Whakaoti i te (12-5)^2+(7-6)^2=r^2

$$( 12 - 5 ) ^ { 2 } + ( 7 - 6 ) ^ { 2 } = r ^ { 2 }$$

Whakaoti mō r

$$r=5\sqrt{2}\approx 7.071067812$$

$$r=-5\sqrt{2}\approx -7.071067812$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 5 i te 12, ka 7.

$$7^{2}+\left(7-6\right)^{2}=r^{2}$$

Tātaihia te 7 mā te pū o 2, kia riro ko 49.

$$49+\left(7-6\right)^{2}=r^{2}$$

Tangohia te 6 i te 7, ka 1.

$$49+1^{2}=r^{2}$$

Tātaihia te 1 mā te pū o 2, kia riro ko 1.

$$49+1=r^{2}$$

Tāpirihia te 49 ki te 1, ka 50.

$$50=r^{2}$$

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

$$r^{2}=50$$

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

$$r=5\sqrt{2} r=-5\sqrt{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 5 i te 12, ka 7.

$$7^{2}+\left(7-6\right)^{2}=r^{2}$$

Tātaihia te 7 mā te pū o 2, kia riro ko 49.

$$49+\left(7-6\right)^{2}=r^{2}$$

Tangohia te 6 i te 7, ka 1.

$$49+1^{2}=r^{2}$$

Tātaihia te 1 mā te pū o 2, kia riro ko 1.

$$49+1=r^{2}$$

Tāpirihia te 49 ki te 1, ka 50.

$$50=r^{2}$$

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

$$r^{2}=50$$

Tangohia te 50 mai i ngā taha e rua.

$$r^{2}-50=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -50 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-50\right)}}{2}$$

Pūrua 0.

$$r=\frac{0±\sqrt{-4\left(-50\right)}}{2}$$

Whakareatia -4 ki te -50.

$$r=\frac{0±\sqrt{200}}{2}$$

Tuhia te pūtakerua o te 200.

$$r=\frac{0±10\sqrt{2}}{2}$$

Nā, me whakaoti te whārite r=\frac{0±10\sqrt{2}}{2} ina he tāpiri te ±.

$$r=5\sqrt{2}$$

Nā, me whakaoti te whārite r=\frac{0±10\sqrt{2}}{2} ina he tango te ±.

$$r=-5\sqrt{2}$$

Kua oti te whārite te whakatau.

$$r=5\sqrt{2} r=-5\sqrt{2}$$