Whakaoti i te 5s^2+(17-5s)^2=49

$$5 s ^ { 2 } + ( 17 - 5 s ) ^ { 2 } = 49$$

Whakaoti mō s

$$s=3$$

$$s = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(17-5s\right)^{2}.

$$5s^{2}+289-170s+25s^{2}=49$$

Pahekotia te 5s^{2} me 25s^{2}, ka 30s^{2}.

$$30s^{2}+289-170s=49$$

Tangohia te 49 mai i ngā taha e rua.

$$30s^{2}+289-170s-49=0$$

Tangohia te 49 i te 289, ka 240.

$$30s^{2}+240-170s=0$$

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.

$$30s^{2}-170s+240=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 30 mō a, -170 mō b, me 240 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{-\left(-170\right)±\sqrt{\left(-170\right)^{2}-4\times 30\times 240}}{2\times 30}$$

Pūrua -170.

$$s=\frac{-\left(-170\right)±\sqrt{28900-4\times 30\times 240}}{2\times 30}$$

Whakareatia -4 ki te 30.

$$s=\frac{-\left(-170\right)±\sqrt{28900-120\times 240}}{2\times 30}$$

Whakareatia -120 ki te 240.

$$s=\frac{-\left(-170\right)±\sqrt{28900-28800}}{2\times 30}$$

Tāpiri 28900 ki te -28800.

$$s=\frac{-\left(-170\right)±\sqrt{100}}{2\times 30}$$

Tuhia te pūtakerua o te 100.

$$s=\frac{-\left(-170\right)±10}{2\times 30}$$

Ko te tauaro o -170 ko 170.

$$s=\frac{170±10}{2\times 30}$$

Whakareatia 2 ki te 30.

$$s=\frac{170±10}{60}$$

Nā, me whakaoti te whārite s=\frac{170±10}{60} ina he tāpiri te ±. Tāpiri 170 ki te 10.

$$s=\frac{180}{60}$$

Whakawehe 180 ki te 60.

$$s=3$$

Nā, me whakaoti te whārite s=\frac{170±10}{60} ina he tango te ±. Tango 10 mai i 170.

$$s=\frac{160}{60}$$

Whakahekea te hautanga \frac{160}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 20.

$$s=\frac{8}{3}$$

Kua oti te whārite te whakatau.

$$s=3 s=\frac{8}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(17-5s\right)^{2}.

$$5s^{2}+289-170s+25s^{2}=49$$

Pahekotia te 5s^{2} me 25s^{2}, ka 30s^{2}.

$$30s^{2}+289-170s=49$$

Tangohia te 289 mai i ngā taha e rua.

$$30s^{2}-170s=49-289$$

Tangohia te 289 i te 49, ka -240.

$$30s^{2}-170s=-240$$

Whakawehea ngā taha e rua ki te 30.

$$\frac{30s^{2}-170s}{30}=-\frac{240}{30}$$

Mā te whakawehe ki te 30 ka wetekia te whakareanga ki te 30.

$$s^{2}+\left(-\frac{170}{30}\right)s=-\frac{240}{30}$$

Whakahekea te hautanga \frac{-170}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$s^{2}-\frac{17}{3}s=-\frac{240}{30}$$

Whakawehe -240 ki te 30.

$$s^{2}-\frac{17}{3}s=-8$$

Whakawehea te -\frac{17}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{17}{6}. Nā, tāpiria te pūrua o te -\frac{17}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$s^{2}-\frac{17}{3}s+\left(-\frac{17}{6}\right)^{2}=-8+\left(-\frac{17}{6}\right)^{2}$$

Pūruatia -\frac{17}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$s^{2}-\frac{17}{3}s+\frac{289}{36}=-8+\frac{289}{36}$$

Tāpiri -8 ki te \frac{289}{36}.

$$s^{2}-\frac{17}{3}s+\frac{289}{36}=\frac{1}{36}$$

Tauwehea s^{2}-\frac{17}{3}s+\frac{289}{36}. 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}.

$$\left(s-\frac{17}{6}\right)^{2}=\frac{1}{36}$$

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

$$\sqrt{\left(s-\frac{17}{6}\right)^{2}}=\sqrt{\frac{1}{36}}$$

Whakarūnātia.

$$s-\frac{17}{6}=\frac{1}{6} s-\frac{17}{6}=-\frac{1}{6}$$

Me tāpiri \frac{17}{6} ki ngā taha e rua o te whārite.

$$s=3 s=\frac{8}{3}$$