Whakaoti i te (x-1)(x-2)+(x-2)=25

$$(x-1)(x-2)+(x-2)=25$$

Whakaoti mō x

$$x=\sqrt{26}+1\approx 6.099019514$$

$$x=1-\sqrt{26}\approx -4.099019514$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$x^{2}-3x+2+x-2=25$$

Pahekotia te -3x me x, ka -2x.

$$x^{2}-2x+2-2=25$$

Tangohia te 2 i te 2, ka 0.

$$x^{2}-2x=25$$

Tangohia te 25 mai i ngā taha e rua.

$$x^{2}-2x-25=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me -25 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-25\right)}}{2}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-25\right)}}{2}$$

Whakareatia -4 ki te -25.

$$x=\frac{-\left(-2\right)±\sqrt{4+100}}{2}$$

Tāpiri 4 ki te 100.

$$x=\frac{-\left(-2\right)±\sqrt{104}}{2}$$

Tuhia te pūtakerua o te 104.

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

Ko te tauaro o -2 ko 2.

$$x=\frac{2±2\sqrt{26}}{2}$$

Nā, me whakaoti te whārite x=\frac{2±2\sqrt{26}}{2} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{26}.

$$x=\frac{2\sqrt{26}+2}{2}$$

Whakawehe 2+2\sqrt{26} ki te 2.

$$x=\sqrt{26}+1$$

Nā, me whakaoti te whārite x=\frac{2±2\sqrt{26}}{2} ina he tango te ±. Tango 2\sqrt{26} mai i 2.

$$x=\frac{2-2\sqrt{26}}{2}$$

Whakawehe 2-2\sqrt{26} ki te 2.

$$x=1-\sqrt{26}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{26}+1 x=1-\sqrt{26}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$x^{2}-3x+2+x-2=25$$

Pahekotia te -3x me x, ka -2x.

$$x^{2}-2x+2-2=25$$

Tangohia te 2 i te 2, ka 0.

$$x^{2}-2x=25$$

Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-2x+1=25+1$$

Tāpiri 25 ki te 1.

$$x^{2}-2x+1=26$$

Tauwehea x^{2}-2x+1. 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}.

$$\left(x-1\right)^{2}=26$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{26}$$

Whakarūnātia.

$$x-1=\sqrt{26} x-1=-\sqrt{26}$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=\sqrt{26}+1 x=1-\sqrt{26}$$