Whakaoti i te x^2-5x+6=x

$$x ^ { 2 } - 5 x + 6 = x$$

Whakaoti mō x

$$x=\sqrt{3}+3\approx 4.732050808$$

$$x=3-\sqrt{3}\approx 1.267949192$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te x mai i ngā taha e rua.

$$x^{2}-5x+6-x=0$$

Pahekotia te -5x me -x, ka -6x.

$$x^{2}-6x+6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -6 mō b, me 6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 6}}{2}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 6}}{2}$$

Whakareatia -4 ki te 6.

$$x=\frac{-\left(-6\right)±\sqrt{36-24}}{2}$$

Tāpiri 36 ki te -24.

$$x=\frac{-\left(-6\right)±\sqrt{12}}{2}$$

Tuhia te pūtakerua o te 12.

$$x=\frac{-\left(-6\right)±2\sqrt{3}}{2}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±2\sqrt{3}}{2}$$

Nā, me whakaoti te whārite x=\frac{6±2\sqrt{3}}{2} ina he tāpiri te ±. Tāpiri 6 ki te 2\sqrt{3}.

$$x=\frac{2\sqrt{3}+6}{2}$$

Whakawehe 6+2\sqrt{3} ki te 2.

$$x=\sqrt{3}+3$$

Nā, me whakaoti te whārite x=\frac{6±2\sqrt{3}}{2} ina he tango te ±. Tango 2\sqrt{3} mai i 6.

$$x=\frac{6-2\sqrt{3}}{2}$$

Whakawehe 6-2\sqrt{3} ki te 2.

$$x=3-\sqrt{3}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{3}+3 x=3-\sqrt{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te x mai i ngā taha e rua.

$$x^{2}-5x+6-x=0$$

Pahekotia te -5x me -x, ka -6x.

$$x^{2}-6x+6=0$$

Tangohia te 6 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-6x=-6$$

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

$$x^{2}-6x+\left(-3\right)^{2}=-6+\left(-3\right)^{2}$$

Pūrua -3.

$$x^{2}-6x+9=-6+9$$

Tāpiri -6 ki te 9.

$$x^{2}-6x+9=3$$

Tauwehea x^{2}-6x+9. 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}.

$$\left(x-3\right)^{2}=3$$

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

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{3}$$

Whakarūnātia.

$$x-3=\sqrt{3} x-3=-\sqrt{3}$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$x=\sqrt{3}+3 x=3-\sqrt{3}$$