Whakaoti i te {l}{x^2+p^2=100}{p-x=-2}

$$\left. \begin{array} { l } { x ^ { 2 } + p ^ { 2 } = 100 } \\ { p - x = - 2 } \end{array} \right.$$

Whakaoti mō x, p

$$x=8\text{, }p=6$$

$$x=-6\text{, }p=-8$$

Ngā Upane e Whakamahi ana i te Whakakapinga me te Tikanga Tātai Pūrua

Hei whakaoti i ētahi whārite takirua mā te whakakapinga, me whakaoti tētahi whārite i te tuatahi mō tētahi o ngā taurangi. Ka whakakapi i te otinga mō taua taurangi ki tērā o ngā whārite.

$$p-x=-2,x^{2}+p^{2}=100$$

Whakaotia te p-x=-2 mō p mā te wehe i te p i te taha mauī o te tohu ōrite.

$$p-x=-2$$

Me tango -x mai i ngā taha e rua o te whārite.

$$p=x-2$$

Whakakapia te x-2 mō te p ki tērā atu whārite, x^{2}+p^{2}=100.

$$x^{2}+\left(x-2\right)^{2}=100$$

Pūrua x-2.

$$x^{2}+x^{2}-4x+4=100$$

Tāpiri x^{2} ki te x^{2}.

$$2x^{2}-4x+4=100$$

Me tango 100 mai i ngā taha e rua o te whārite.

$$2x^{2}-4x-96=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1+1\times 1^{2} mō a, 1\left(-2\right)\times 1\times 2 mō b, me -96 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 2\left(-96\right)}}{2\times 2}$$

Pūrua 1\left(-2\right)\times 1\times 2.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 2\left(-96\right)}}{2\times 2}$$

Whakareatia -4 ki te 1+1\times 1^{2}.

$$x=\frac{-\left(-4\right)±\sqrt{16-8\left(-96\right)}}{2\times 2}$$

Whakareatia -8 ki te -96.

$$x=\frac{-\left(-4\right)±\sqrt{16+768}}{2\times 2}$$

Tāpiri 16 ki te 768.

$$x=\frac{-\left(-4\right)±\sqrt{784}}{2\times 2}$$

Tuhia te pūtakerua o te 784.

$$x=\frac{-\left(-4\right)±28}{2\times 2}$$

Ko te tauaro o 1\left(-2\right)\times 1\times 2 ko 4.

$$x=\frac{4±28}{2\times 2}$$

Whakareatia 2 ki te 1+1\times 1^{2}.

$$x=\frac{4±28}{4}$$

Nā, me whakaoti te whārite x=\frac{4±28}{4} ina he tāpiri te ±. Tāpiri 4 ki te 28.

$$x=\frac{32}{4}$$

Whakawehe 32 ki te 4.

$$x=8$$

Nā, me whakaoti te whārite x=\frac{4±28}{4} ina he tango te ±. Tango 28 mai i 4.

$$x=-\frac{24}{4}$$

Whakawehe -24 ki te 4.

$$x=-6$$

E rua ngā otinga mō x: 8 me -6. Me whakakapi 8 mō x ki te whārite p=x-2 hei kimi i te otinga hāngai mō p e pai ai ki ngā whārite e rua.

$$p=8-2$$

Tāpiri 1\times 8 ki te -2.

$$p=6$$

Me whakakapi te -6 ināianei mō te x ki te whārite p=x-2 ka whakaoti hei kimi i te otinga hāngai mō p e pai ai ki ngā whārite e rua.

$$p=-6-2$$

Tāpiri -6 ki te -2.

$$p=-8$$

Kua oti te pūnaha te whakatau.

$$p=6,x=8\text{ or }p=-8,x=-6$$