Whakaoti i te (1+x)(1+2x)=1.32

$$(1+x)(1+2x)=1.32$$

Whakaoti mō x

$$x=0.1$$

$$x=-1.6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 1+x ki te 1+2x ka whakakotahi i ngā kupu rite.

$$1+3x+2x^{2}=1.32$$

Tangohia te 1.32 mai i ngā taha e rua.

$$1+3x+2x^{2}-1.32=0$$

Tangohia te 1.32 i te 1, ka -0.32.

$$-0.32+3x+2x^{2}=0$$

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.

$$2x^{2}+3x-0.32=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 3 mō b, me -0.32 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\times 2\left(-0.32\right)}}{2\times 2}$$

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\times 2\left(-0.32\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-3±\sqrt{9-8\left(-0.32\right)}}{2\times 2}$$

Whakareatia -8 ki te -0.32.

$$x=\frac{-3±\sqrt{9+2.56}}{2\times 2}$$

Tāpiri 9 ki te 2.56.

$$x=\frac{-3±\sqrt{11.56}}{2\times 2}$$

Tuhia te pūtakerua o te 11.56.

$$x=\frac{-3±\frac{17}{5}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-3±\frac{17}{5}}{4}$$

Nā, me whakaoti te whārite x=\frac{-3±\frac{17}{5}}{4} ina he tāpiri te ±. Tāpiri -3 ki te \frac{17}{5}.

$$x=\frac{\frac{2}{5}}{4}$$

Whakawehe \frac{2}{5} ki te 4.

$$x=\frac{1}{10}$$

Nā, me whakaoti te whārite x=\frac{-3±\frac{17}{5}}{4} ina he tango te ±. Tango \frac{17}{5} mai i -3.

$$x=-\frac{\frac{32}{5}}{4}$$

Whakawehe -\frac{32}{5} ki te 4.

$$x=-\frac{8}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{10} x=-\frac{8}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 1+x ki te 1+2x ka whakakotahi i ngā kupu rite.

$$1+3x+2x^{2}=1.32$$

Tangohia te 1 mai i ngā taha e rua.

$$3x+2x^{2}=1.32-1$$

Tangohia te 1 i te 1.32, ka 0.32.

$$3x+2x^{2}=0.32$$

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.

$$2x^{2}+3x=0.32$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+3x}{2}=\frac{0.32}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\frac{3}{2}x=\frac{0.32}{2}$$

Whakawehe 0.32 ki te 2.

$$x^{2}+\frac{3}{2}x=0.16$$

Whakawehea te \frac{3}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{4}. Nā, tāpiria te pūrua o te \frac{3}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{3}{2}x+\left(\frac{3}{4}\right)^{2}=0.16+\left(\frac{3}{4}\right)^{2}$$

Pūruatia \frac{3}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{3}{2}x+\frac{9}{16}=0.16+\frac{9}{16}$$

Tāpiri 0.16 ki te \frac{9}{16} 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.

$$x^{2}+\frac{3}{2}x+\frac{9}{16}=\frac{289}{400}$$

Tauwehea x^{2}+\frac{3}{2}x+\frac{9}{16}. 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}.

$$\left(x+\frac{3}{4}\right)^{2}=\frac{289}{400}$$

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

$$\sqrt{\left(x+\frac{3}{4}\right)^{2}}=\sqrt{\frac{289}{400}}$$

Whakarūnātia.

$$x+\frac{3}{4}=\frac{17}{20} x+\frac{3}{4}=-\frac{17}{20}$$

Me tango \frac{3}{4} mai i ngā taha e rua o te whārite.

$$x=\frac{1}{10} x=-\frac{8}{5}$$