Whakaoti i te (x-5)^2=1

$$( x - 5 ) ^ { 2 } = 1$$

Whakaoti mō x

$$x=6$$

$$x=4$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-5\right)^{2}.

$$x^{2}-10x+25=1$$

Tangohia te 1 mai i ngā taha e rua.

$$x^{2}-10x+25-1=0$$

Tangohia te 1 i te 25, ka 24.

$$x^{2}-10x+24=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}-10x+24 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-10 ab=24$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 24.

$$-1,-24 -2,-12 -3,-8 -4,-6$$

Tātaihia te tapeke mō ia takirua.

$$-1-24=-25 -2-12=-14 -3-8=-11 -4-6=-10$$

Ko te otinga te takirua ka hoatu i te tapeke -10.

$$a=-6 b=-4$$

Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.

$$\left(x-6\right)\left(x-4\right)$$

Hei kimi otinga whārite, me whakaoti te x-6=0 me te x-4=0.

$$x=6 x=4$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-5\right)^{2}.

$$x^{2}-10x+25=1$$

Tangohia te 1 mai i ngā taha e rua.

$$x^{2}-10x+25-1=0$$

Tangohia te 1 i te 25, ka 24.

$$x^{2}-10x+24=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+24. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-10 ab=1\times 24=24$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 24.

$$-1,-24 -2,-12 -3,-8 -4,-6$$

Tātaihia te tapeke mō ia takirua.

$$-1-24=-25 -2-12=-14 -3-8=-11 -4-6=-10$$

Ko te otinga te takirua ka hoatu i te tapeke -10.

$$a=-6 b=-4$$

Tuhia anō te x^{2}-10x+24 hei \left(x^{2}-6x\right)+\left(-4x+24\right).

$$\left(x^{2}-6x\right)+\left(-4x+24\right)$$

Tauwehea te x i te tuatahi me te -4 i te rōpū tuarua.

$$x\left(x-6\right)-4\left(x-6\right)$$

Whakatauwehea atu te kīanga pātahi x-6 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-6\right)\left(x-4\right)$$

Hei kimi otinga whārite, me whakaoti te x-6=0 me te x-4=0.

$$x=6 x=4$$

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-5\right)^{2}.

$$x^{2}-10x+25=1$$

Tangohia te 1 mai i ngā taha e rua.

$$x^{2}-10x+25-1=0$$

Tangohia te 1 i te 25, ka 24.

$$x^{2}-10x+24=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -10 mō b, me 24 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 24}}{2}$$

Pūrua -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times 24}}{2}$$

Whakareatia -4 ki te 24.

$$x=\frac{-\left(-10\right)±\sqrt{100-96}}{2}$$

Tāpiri 100 ki te -96.

$$x=\frac{-\left(-10\right)±\sqrt{4}}{2}$$

Tuhia te pūtakerua o te 4.

$$x=\frac{-\left(-10\right)±2}{2}$$

Ko te tauaro o -10 ko 10.

$$x=\frac{10±2}{2}$$

Nā, me whakaoti te whārite x=\frac{10±2}{2} ina he tāpiri te ±. Tāpiri 10 ki te 2.

$$x=\frac{12}{2}$$

Whakawehe 12 ki te 2.

$$x=6$$

Nā, me whakaoti te whārite x=\frac{10±2}{2} ina he tango te ±. Tango 2 mai i 10.

$$x=\frac{8}{2}$$

Whakawehe 8 ki te 2.

$$x=4$$

Kua oti te whārite te whakatau.

$$x=6 x=4$$

Ngā Upane mō te Whakaoti i te Pūrua

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

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

Whakarūnātia.

$$x-5=1 x-5=-1$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$x=6 x=4$$