Whakaoti i te 35r^2-72r+36=0

$$35 r ^ { 2 } - 72 r + 36 = 0$$

Whakaoti mō r

$$r=\frac{6}{7}\approx 0.857142857$$

$$r = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$35r^{2}-72r+36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 35 mō a, -72 mō b, me 36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}-4\times 35\times 36}}{2\times 35}$$

Pūrua -72.

$$r=\frac{-\left(-72\right)±\sqrt{5184-4\times 35\times 36}}{2\times 35}$$

Whakareatia -4 ki te 35.

$$r=\frac{-\left(-72\right)±\sqrt{5184-140\times 36}}{2\times 35}$$

Whakareatia -140 ki te 36.

$$r=\frac{-\left(-72\right)±\sqrt{5184-5040}}{2\times 35}$$

Tāpiri 5184 ki te -5040.

$$r=\frac{-\left(-72\right)±\sqrt{144}}{2\times 35}$$

Tuhia te pūtakerua o te 144.

$$r=\frac{-\left(-72\right)±12}{2\times 35}$$

Ko te tauaro o -72 ko 72.

$$r=\frac{72±12}{2\times 35}$$

Whakareatia 2 ki te 35.

$$r=\frac{72±12}{70}$$

Nā, me whakaoti te whārite r=\frac{72±12}{70} ina he tāpiri te ±. Tāpiri 72 ki te 12.

$$r=\frac{84}{70}$$

Whakahekea te hautanga \frac{84}{70} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

$$r=\frac{6}{5}$$

Nā, me whakaoti te whārite r=\frac{72±12}{70} ina he tango te ±. Tango 12 mai i 72.

$$r=\frac{60}{70}$$

Whakahekea te hautanga \frac{60}{70} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$r=\frac{6}{7}$$

Kua oti te whārite te whakatau.

$$r=\frac{6}{5} r=\frac{6}{7}$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$35r^{2}-72r+36=0$$

Me tango 36 mai i ngā taha e rua o te whārite.

$$35r^{2}-72r+36-36=-36$$

Mā te tango i te 36 i a ia ake anō ka toe ko te 0.

$$35r^{2}-72r=-36$$

Whakawehea ngā taha e rua ki te 35.

$$\frac{35r^{2}-72r}{35}=-\frac{36}{35}$$

Mā te whakawehe ki te 35 ka wetekia te whakareanga ki te 35.

$$r^{2}-\frac{72}{35}r=-\frac{36}{35}$$

Whakawehea te -\frac{72}{35}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{36}{35}. Nā, tāpiria te pūrua o te -\frac{36}{35} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$r^{2}-\frac{72}{35}r+\left(-\frac{36}{35}\right)^{2}=-\frac{36}{35}+\left(-\frac{36}{35}\right)^{2}$$

Pūruatia -\frac{36}{35} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$r^{2}-\frac{72}{35}r+\frac{1296}{1225}=-\frac{36}{35}+\frac{1296}{1225}$$

Tāpiri -\frac{36}{35} ki te \frac{1296}{1225} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$r^{2}-\frac{72}{35}r+\frac{1296}{1225}=\frac{36}{1225}$$

Tauwehea r^{2}-\frac{72}{35}r+\frac{1296}{1225}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(r-\frac{36}{35}\right)^{2}=\frac{36}{1225}$$

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

$$\sqrt{\left(r-\frac{36}{35}\right)^{2}}=\sqrt{\frac{36}{1225}}$$

Whakarūnātia.

$$r-\frac{36}{35}=\frac{6}{35} r-\frac{36}{35}=-\frac{6}{35}$$

Me tāpiri \frac{36}{35} ki ngā taha e rua o te whārite.

$$r=\frac{6}{5} r=\frac{6}{7}$$