Whakaoti i te 3left(x+1right)^2=75

$$3 { \left(x+1 \right) }^{ 2 } =75$$

Whakaoti mō x

$$x=4$$

$$x=-6$$

Ngā Upane Whakamahi Tauwehe

Whakawehea ngā taha e rua ki te 3.

$$\left(x+1\right)^{2}=\frac{75}{3}$$

Whakawehea te 75 ki te 3, kia riro ko 25.

$$\left(x+1\right)^{2}=25$$

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

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

Tangohia te 25 mai i ngā taha e rua.

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

Tangohia te 25 i te 1, ka -24.

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

Hei whakaoti i te whārite, whakatauwehea te x^{2}+2x-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.

$$a+b=2 ab=-24$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. 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.

$$-1+24=23 -2+12=10 -3+8=5 -4+6=2$$

Ko te otinga te takirua ka hoatu i te tapeke 2.

$$a=-4 b=6$$

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

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

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

$$x=4 x=-6$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakawehea ngā taha e rua ki te 3.

$$\left(x+1\right)^{2}=\frac{75}{3}$$

Whakawehea te 75 ki te 3, kia riro ko 25.

$$\left(x+1\right)^{2}=25$$

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

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

Tangohia te 25 mai i ngā taha e rua.

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

Tangohia te 25 i te 1, ka -24.

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

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.

$$a+b=2 ab=1\left(-24\right)=-24$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. 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.

$$-1+24=23 -2+12=10 -3+8=5 -4+6=2$$

Ko te otinga te takirua ka hoatu i te tapeke 2.

$$a=-4 b=6$$

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

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

Tauwehea te x i te tuatahi me te 6 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi x-4 mā te whakamahi i te āhuatanga tātai tohatoha.

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

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

$$x=4 x=-6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ngā taha e rua ki te 3.

$$\left(x+1\right)^{2}=\frac{75}{3}$$

Whakawehea te 75 ki te 3, kia riro ko 25.

$$\left(x+1\right)^{2}=25$$

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

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

Tangohia te 25 mai i ngā taha e rua.

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

Tangohia te 25 i te 1, ka -24.

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

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

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

Pūrua 2.

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

Whakareatia -4 ki te -24.

$$x=\frac{-2±\sqrt{4+96}}{2}$$

Tāpiri 4 ki te 96.

$$x=\frac{-2±\sqrt{100}}{2}$$

Tuhia te pūtakerua o te 100.

$$x=\frac{-2±10}{2}$$

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

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

Whakawehe 8 ki te 2.

$$x=4$$

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

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

Whakawehe -12 ki te 2.

$$x=-6$$

Kua oti te whārite te whakatau.

$$x=4 x=-6$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawehea ngā taha e rua ki te 3.

$$\left(x+1\right)^{2}=\frac{75}{3}$$

Whakawehea te 75 ki te 3, kia riro ko 25.

$$\left(x+1\right)^{2}=25$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{25}$$

Whakarūnātia.

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

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=4 x=-6$$