Whakaoti i te x^2+2/3+x+7/12=1+x^2+1/4

$$\frac { x ^ { 2 } + 2 } { 3 } + \frac { x + 7 } { 12 } = 1 + \frac { x ^ { 2 } + 1 } { 4 }$$

Whakaoti mō x

$$x=-1$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 3,12,4.

$$4\left(x^{2}+2\right)+x+7=12+3\left(x^{2}+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x^{2}+2.

$$4x^{2}+8+x+7=12+3\left(x^{2}+1\right)$$

Tāpirihia te 8 ki te 7, ka 15.

$$4x^{2}+15+x=12+3\left(x^{2}+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}+1.

$$4x^{2}+15+x=12+3x^{2}+3$$

Tāpirihia te 12 ki te 3, ka 15.

$$4x^{2}+15+x=15+3x^{2}$$

Tangohia te 15 mai i ngā taha e rua.

$$4x^{2}+15+x-15=3x^{2}$$

Tangohia te 15 i te 15, ka 0.

$$4x^{2}+x=3x^{2}$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$4x^{2}+x-3x^{2}=0$$

Pahekotia te 4x^{2} me -3x^{2}, ka x^{2}.

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

Tauwehea te x.

$$x\left(x+1\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te x+1=0.

$$x=0 x=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 3,12,4.

$$4\left(x^{2}+2\right)+x+7=12+3\left(x^{2}+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x^{2}+2.

$$4x^{2}+8+x+7=12+3\left(x^{2}+1\right)$$

Tāpirihia te 8 ki te 7, ka 15.

$$4x^{2}+15+x=12+3\left(x^{2}+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}+1.

$$4x^{2}+15+x=12+3x^{2}+3$$

Tāpirihia te 12 ki te 3, ka 15.

$$4x^{2}+15+x=15+3x^{2}$$

Tangohia te 15 mai i ngā taha e rua.

$$4x^{2}+15+x-15=3x^{2}$$

Tangohia te 15 i te 15, ka 0.

$$4x^{2}+x=3x^{2}$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$4x^{2}+x-3x^{2}=0$$

Pahekotia te 4x^{2} me -3x^{2}, ka x^{2}.

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

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

$$x=\frac{-1±\sqrt{1^{2}}}{2}$$

Tuhia te pūtakerua o te 1^{2}.

$$x=\frac{-1±1}{2}$$

Nā, me whakaoti te whārite x=\frac{-1±1}{2} ina he tāpiri te ±. Tāpiri -1 ki te 1.

$$x=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-1±1}{2} ina he tango te ±. Tango 1 mai i -1.

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

Whakawehe -2 ki te 2.

$$x=-1$$

Kua oti te whārite te whakatau.

$$x=0 x=-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 3,12,4.

$$4\left(x^{2}+2\right)+x+7=12+3\left(x^{2}+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x^{2}+2.

$$4x^{2}+8+x+7=12+3\left(x^{2}+1\right)$$

Tāpirihia te 8 ki te 7, ka 15.

$$4x^{2}+15+x=12+3\left(x^{2}+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}+1.

$$4x^{2}+15+x=12+3x^{2}+3$$

Tāpirihia te 12 ki te 3, ka 15.

$$4x^{2}+15+x=15+3x^{2}$$

Tangohia te 15 mai i ngā taha e rua.

$$4x^{2}+15+x-15=3x^{2}$$

Tangohia te 15 i te 15, ka 0.

$$4x^{2}+x=3x^{2}$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$4x^{2}+x-3x^{2}=0$$

Pahekotia te 4x^{2} me -3x^{2}, ka x^{2}.

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

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

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=\left(\frac{1}{2}\right)^{2}$$

Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+x+\frac{1}{4}=\frac{1}{4}$$

Tauwehea te x^{2}+x+\frac{1}{4}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{1}{4}$$

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

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Whakarūnātia.

$$x+\frac{1}{2}=\frac{1}{2} x+\frac{1}{2}=-\frac{1}{2}$$

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

$$x=0 x=-1$$