Whakaoti i te (11+x)^2+(11-x)^2=120

$$( 11 + x ) ^ { 2 } + ( 11 - x ) ^ { 2 } = 120$$

Whakaoti mō x (complex solution)

$$x=-\sqrt{61}i\approx -0-7.810249676i$$

$$x=\sqrt{61}i\approx 7.810249676i$$

Ngā Upane mā te Kimi Pūtakerua

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(11+x\right)^{2}.

$$121+22x+x^{2}+\left(11-x\right)^{2}=120$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(11-x\right)^{2}.

$$121+22x+x^{2}+121-22x+x^{2}=120$$

Tāpirihia te 121 ki te 121, ka 242.

$$242+22x+x^{2}-22x+x^{2}=120$$

Pahekotia te 22x me -22x, ka 0.

$$242+x^{2}+x^{2}=120$$

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

$$242+2x^{2}=120$$

Tangohia te 242 mai i ngā taha e rua.

$$2x^{2}=120-242$$

Tangohia te 242 i te 120, ka -122.

$$2x^{2}=-122$$

Whakawehea ngā taha e rua ki te 2.

$$x^{2}=\frac{-122}{2}$$

Whakawehea te -122 ki te 2, kia riro ko -61.

$$x^{2}=-61$$

Kua oti te whārite te whakatau.

$$x=\sqrt{61}i x=-\sqrt{61}i$$

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(11+x\right)^{2}.

$$121+22x+x^{2}+\left(11-x\right)^{2}=120$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(11-x\right)^{2}.

$$121+22x+x^{2}+121-22x+x^{2}=120$$

Tāpirihia te 121 ki te 121, ka 242.

$$242+22x+x^{2}-22x+x^{2}=120$$

Pahekotia te 22x me -22x, ka 0.

$$242+x^{2}+x^{2}=120$$

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

$$242+2x^{2}=120$$

Tangohia te 120 mai i ngā taha e rua.

$$242+2x^{2}-120=0$$

Tangohia te 120 i te 242, ka 122.

$$122+2x^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$2x^{2}+122=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me 122 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 122}}{2\times 2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 2\times 122}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\times 122}}{2\times 2}$$

Whakareatia -8 ki te 122.

$$x=\frac{0±\sqrt{-976}}{2\times 2}$$

Tuhia te pūtakerua o te -976.

$$x=\frac{0±4\sqrt{61}i}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±4\sqrt{61}i}{4}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{61}i}{4} ina he tāpiri te ±.

$$x=\sqrt{61}i$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{61}i}{4} ina he tango te ±.

$$x=-\sqrt{61}i$$

Kua oti te whārite te whakatau.

$$x=\sqrt{61}i x=-\sqrt{61}i$$