Whakaoti i te 16x^2-26x+3

$$16 x ^ { 2 } - 26 x + 3$$

Tauwehe

$$\left(2x-3\right)\left(8x-1\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 16x^{2}+ax+bx+3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-26 ab=16\times 3=48$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 48.

$$-1,-48 -2,-24 -3,-16 -4,-12 -6,-8$$

Tātaihia te tapeke mō ia takirua.

$$-1-48=-49 -2-24=-26 -3-16=-19 -4-12=-16 -6-8=-14$$

Ko te otinga te takirua ka hoatu i te tapeke -26.

$$a=-24 b=-2$$

Tuhia anō te 16x^{2}-26x+3 hei \left(16x^{2}-24x\right)+\left(-2x+3\right).

$$\left(16x^{2}-24x\right)+\left(-2x+3\right)$$

Tauwehea te 8x i te tuatahi me te -1 i te rōpū tuarua.

$$8x\left(2x-3\right)-\left(2x-3\right)$$

Whakatauwehea atu te kīanga pātahi 2x-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2x-3\right)\left(8x-1\right)$$

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.

$$16x^{2}-26x+3=0$$

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.

$$x=\frac{-\left(-26\right)±\sqrt{\left(-26\right)^{2}-4\times 16\times 3}}{2\times 16}$$

Pūrua -26.

$$x=\frac{-\left(-26\right)±\sqrt{676-4\times 16\times 3}}{2\times 16}$$

Whakareatia -4 ki te 16.

$$x=\frac{-\left(-26\right)±\sqrt{676-64\times 3}}{2\times 16}$$

Whakareatia -64 ki te 3.

$$x=\frac{-\left(-26\right)±\sqrt{676-192}}{2\times 16}$$

Tāpiri 676 ki te -192.

$$x=\frac{-\left(-26\right)±\sqrt{484}}{2\times 16}$$

Tuhia te pūtakerua o te 484.

$$x=\frac{-\left(-26\right)±22}{2\times 16}$$

Ko te tauaro o -26 ko 26.

$$x=\frac{26±22}{2\times 16}$$

Whakareatia 2 ki te 16.

$$x=\frac{26±22}{32}$$

Nā, me whakaoti te whārite x=\frac{26±22}{32} ina he tāpiri te ±. Tāpiri 26 ki te 22.

$$x=\frac{48}{32}$$

Whakahekea te hautanga \frac{48}{32} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 16.

$$x=\frac{3}{2}$$

Nā, me whakaoti te whārite x=\frac{26±22}{32} ina he tango te ±. Tango 22 mai i 26.

$$x=\frac{4}{32}$$

Whakahekea te hautanga \frac{4}{32} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

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{3}{2} mō te x_{1} me te \frac{1}{8} mō te x_{2}.

$$16x^{2}-26x+3=16\left(x-\frac{3}{2}\right)\left(x-\frac{1}{8}\right)$$

Tango \frac{3}{2} mai i x 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.

$$16x^{2}-26x+3=16\times \frac{2x-3}{2}\left(x-\frac{1}{8}\right)$$

Tango \frac{1}{8} mai i x 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.

$$16x^{2}-26x+3=16\times \frac{2x-3}{2}\times \frac{8x-1}{8}$$

Whakareatia \frac{2x-3}{2} ki te \frac{8x-1}{8} 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.

$$16x^{2}-26x+3=16\times \frac{\left(2x-3\right)\left(8x-1\right)}{2\times 8}$$

Whakareatia 2 ki te 8.

$$16x^{2}-26x+3=16\times \frac{\left(2x-3\right)\left(8x-1\right)}{16}$$

Whakakorea atu te tauwehe pūnoa nui rawa 16 i roto i te 16 me te 16.

$$16x^{2}-26x+3=\left(2x-3\right)\left(8x-1\right)$$

Aromātai

$$\left(2x-3\right)\left(8x-1\right)$$