Whakaoti i te 56s^2+17s-3

$$56 s ^ { 2 } + 17 s - 3$$

Tauwehe

$$\left(8s-1\right)\left(7s+3\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 56s^{2}+as+bs-3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=17 ab=56\left(-3\right)=-168$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -168.

$$-1,168 -2,84 -3,56 -4,42 -6,28 -7,24 -8,21 -12,14$$

Tātaihia te tapeke mō ia takirua.

$$-1+168=167 -2+84=82 -3+56=53 -4+42=38 -6+28=22 -7+24=17 -8+21=13 -12+14=2$$

Ko te otinga te takirua ka hoatu i te tapeke 17.

$$a=-7 b=24$$

Tuhia anō te 56s^{2}+17s-3 hei \left(56s^{2}-7s\right)+\left(24s-3\right).

$$\left(56s^{2}-7s\right)+\left(24s-3\right)$$

Tauwehea te 7s i te tuatahi me te 3 i te rōpū tuarua.

$$7s\left(8s-1\right)+3\left(8s-1\right)$$

Whakatauwehea atu te kīanga pātahi 8s-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(8s-1\right)\left(7s+3\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$56s^{2}+17s-3=0$$

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.

$$s=\frac{-17±\sqrt{17^{2}-4\times 56\left(-3\right)}}{2\times 56}$$

Pūrua 17.

$$s=\frac{-17±\sqrt{289-4\times 56\left(-3\right)}}{2\times 56}$$

Whakareatia -4 ki te 56.

$$s=\frac{-17±\sqrt{289-224\left(-3\right)}}{2\times 56}$$

Whakareatia -224 ki te -3.

$$s=\frac{-17±\sqrt{289+672}}{2\times 56}$$

Tāpiri 289 ki te 672.

$$s=\frac{-17±\sqrt{961}}{2\times 56}$$

Tuhia te pūtakerua o te 961.

$$s=\frac{-17±31}{2\times 56}$$

Whakareatia 2 ki te 56.

$$s=\frac{-17±31}{112}$$

Nā, me whakaoti te whārite s=\frac{-17±31}{112} ina he tāpiri te ±. Tāpiri -17 ki te 31.

$$s=\frac{14}{112}$$

Whakahekea te hautanga \frac{14}{112} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

$$s=\frac{1}{8}$$

Nā, me whakaoti te whārite s=\frac{-17±31}{112} ina he tango te ±. Tango 31 mai i -17.

$$s=-\frac{48}{112}$$

Whakahekea te hautanga \frac{-48}{112} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 16.

$$s=-\frac{3}{7}$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te \frac{1}{8} mō te x_{1} me te -\frac{3}{7} mō te x_{2}.

$$56s^{2}+17s-3=56\left(s-\frac{1}{8}\right)\left(s-\left(-\frac{3}{7}\right)\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$56s^{2}+17s-3=56\left(s-\frac{1}{8}\right)\left(s+\frac{3}{7}\right)$$

Tango \frac{1}{8} mai i s mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$56s^{2}+17s-3=56\times \frac{8s-1}{8}\left(s+\frac{3}{7}\right)$$

Tāpiri \frac{3}{7} ki te s 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.

$$56s^{2}+17s-3=56\times \frac{8s-1}{8}\times \frac{7s+3}{7}$$

Whakareatia \frac{8s-1}{8} ki te \frac{7s+3}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$56s^{2}+17s-3=56\times \frac{\left(8s-1\right)\left(7s+3\right)}{8\times 7}$$

Whakareatia 8 ki te 7.

$$56s^{2}+17s-3=56\times \frac{\left(8s-1\right)\left(7s+3\right)}{56}$$

Whakakorea atu te tauwehe pūnoa nui rawa 56 i roto i te 56 me te 56.

$$56s^{2}+17s-3=\left(8s-1\right)\left(7s+3\right)$$

Aromātai

$$\left(8s-1\right)\left(7s+3\right)$$