Whakaoti i te 144/169=r^2

$$\frac { 144 } { 169 } = r ^ { 2 }$$

Whakaoti mō r

$$r=\frac{12}{13}\approx 0.923076923$$

$$r=-\frac{12}{13}\approx -0.923076923$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

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

$$r^{2}=\frac{144}{169}$$

Tangohia te \frac{144}{169} mai i ngā taha e rua.

$$r^{2}-\frac{144}{169}=0$$

Me whakarea ngā taha e rua ki te 169.

$$169r^{2}-144=0$$

Whakaarohia te 169r^{2}-144. Tuhia anō te 169r^{2}-144 hei \left(13r\right)^{2}-12^{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).

$$\left(13r-12\right)\left(13r+12\right)=0$$

Hei kimi otinga whārite, me whakaoti te 13r-12=0 me te 13r+12=0.

$$r=\frac{12}{13} r=-\frac{12}{13}$$

Ngā Upane mā te Kimi Pūtakerua

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

$$r^{2}=\frac{144}{169}$$

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

$$r=\frac{12}{13} r=-\frac{12}{13}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$r^{2}=\frac{144}{169}$$

Tangohia te \frac{144}{169} mai i ngā taha e rua.

$$r^{2}-\frac{144}{169}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -\frac{144}{169} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-\frac{144}{169}\right)}}{2}$$

Pūrua 0.

$$r=\frac{0±\sqrt{-4\left(-\frac{144}{169}\right)}}{2}$$

Whakareatia -4 ki te -\frac{144}{169}.

$$r=\frac{0±\sqrt{\frac{576}{169}}}{2}$$

Tuhia te pūtakerua o te \frac{576}{169}.

$$r=\frac{0±\frac{24}{13}}{2}$$

Nā, me whakaoti te whārite r=\frac{0±\frac{24}{13}}{2} ina he tāpiri te ±.

$$r=\frac{12}{13}$$

Nā, me whakaoti te whārite r=\frac{0±\frac{24}{13}}{2} ina he tango te ±.

$$r=-\frac{12}{13}$$

Kua oti te whārite te whakatau.

$$r=\frac{12}{13} r=-\frac{12}{13}$$