Whakaoti i te left(x-2right)^2+left(x-1right)^2+x^2=left(x+1right)^2+{left(x+2right)}^2

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

Whakaoti mō x

$$x=12$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-2\right)^{2}.

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-1\right)^{2}.

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

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

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

Pahekotia te -4x me -2x, ka -6x.

$$2x^{2}-6x+4+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Tāpirihia te 4 ki te 1, ka 5.

$$2x^{2}-6x+5+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

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

$$3x^{2}-6x+5=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$3x^{2}-6x+5=x^{2}+2x+1+\left(x+2\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+2\right)^{2}.

$$3x^{2}-6x+5=x^{2}+2x+1+x^{2}+4x+4$$

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

$$3x^{2}-6x+5=2x^{2}+2x+1+4x+4$$

Pahekotia te 2x me 4x, ka 6x.

$$3x^{2}-6x+5=2x^{2}+6x+1+4$$

Tāpirihia te 1 ki te 4, ka 5.

$$3x^{2}-6x+5=2x^{2}+6x+5$$

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

$$3x^{2}-6x+5-2x^{2}=6x+5$$

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

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

Tangohia te 6x mai i ngā taha e rua.

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

Pahekotia te -6x me -6x, ka -12x.

$$x^{2}-12x+5=5$$

Tangohia te 5 mai i ngā taha e rua.

$$x^{2}-12x+5-5=0$$

Tangohia te 5 i te 5, ka 0.

$$x^{2}-12x=0$$

Tauwehea te x.

$$x\left(x-12\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te x-12=0.

$$x=0 x=12$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-2\right)^{2}.

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-1\right)^{2}.

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

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

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

Pahekotia te -4x me -2x, ka -6x.

$$2x^{2}-6x+4+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Tāpirihia te 4 ki te 1, ka 5.

$$2x^{2}-6x+5+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

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

$$3x^{2}-6x+5=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$3x^{2}-6x+5=x^{2}+2x+1+\left(x+2\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+2\right)^{2}.

$$3x^{2}-6x+5=x^{2}+2x+1+x^{2}+4x+4$$

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

$$3x^{2}-6x+5=2x^{2}+2x+1+4x+4$$

Pahekotia te 2x me 4x, ka 6x.

$$3x^{2}-6x+5=2x^{2}+6x+1+4$$

Tāpirihia te 1 ki te 4, ka 5.

$$3x^{2}-6x+5=2x^{2}+6x+5$$

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

$$3x^{2}-6x+5-2x^{2}=6x+5$$

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

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

Tangohia te 6x mai i ngā taha e rua.

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

Pahekotia te -6x me -6x, ka -12x.

$$x^{2}-12x+5=5$$

Tangohia te 5 mai i ngā taha e rua.

$$x^{2}-12x+5-5=0$$

Tangohia te 5 i te 5, ka 0.

$$x^{2}-12x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -12 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Tuhia te pūtakerua o te \left(-12\right)^{2}.

$$x=\frac{-\left(-12\right)±12}{2}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±12}{2}$$

Nā, me whakaoti te whārite x=\frac{12±12}{2} ina he tāpiri te ±. Tāpiri 12 ki te 12.

$$x=\frac{24}{2}$$

Whakawehe 24 ki te 2.

$$x=12$$

Nā, me whakaoti te whārite x=\frac{12±12}{2} ina he tango te ±. Tango 12 mai i 12.

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

Whakawehe 0 ki te 2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=12 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-2\right)^{2}.

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-1\right)^{2}.

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

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

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

Pahekotia te -4x me -2x, ka -6x.

$$2x^{2}-6x+4+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Tāpirihia te 4 ki te 1, ka 5.

$$2x^{2}-6x+5+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

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

$$3x^{2}-6x+5=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$3x^{2}-6x+5=x^{2}+2x+1+\left(x+2\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+2\right)^{2}.

$$3x^{2}-6x+5=x^{2}+2x+1+x^{2}+4x+4$$

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

$$3x^{2}-6x+5=2x^{2}+2x+1+4x+4$$

Pahekotia te 2x me 4x, ka 6x.

$$3x^{2}-6x+5=2x^{2}+6x+1+4$$

Tāpirihia te 1 ki te 4, ka 5.

$$3x^{2}-6x+5=2x^{2}+6x+5$$

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

$$3x^{2}-6x+5-2x^{2}=6x+5$$

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

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

Tangohia te 6x mai i ngā taha e rua.

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

Pahekotia te -6x me -6x, ka -12x.

$$x^{2}-12x+5=5$$

Tangohia te 5 mai i ngā taha e rua.

$$x^{2}-12x+5-5=0$$

Tangohia te 5 i te 5, ka 0.

$$x^{2}-12x=0$$

Whakawehea te -12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -6. Nā, tāpiria te pūrua o te -6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-12x+\left(-6\right)^{2}=\left(-6\right)^{2}$$

Pūrua -6.

$$x^{2}-12x+36=36$$

Tauwehea x^{2}-12x+36. 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}.

$$\left(x-6\right)^{2}=36$$

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

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{36}$$

Whakarūnātia.

$$x-6=6 x-6=-6$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$x=12 x=0$$