Whakaoti i te sqrt{31-x}=x-1

$$\sqrt { 31 - x } = x - 1$$

Whakaoti mō x

$$x=6$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{31-x}\right)^{2}=\left(x-1\right)^{2}$$

Tātaihia te \sqrt{31-x} mā te pū o 2, kia riro ko 31-x.

$$31-x=\left(x-1\right)^{2}$$

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

$$31-x=x^{2}-2x+1$$

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

$$31-x-x^{2}=-2x+1$$

Me tāpiri te 2x ki ngā taha e rua.

$$31-x-x^{2}+2x=1$$

Pahekotia te -x me 2x, ka x.

$$31+x-x^{2}=1$$

Tangohia te 1 mai i ngā taha e rua.

$$31+x-x^{2}-1=0$$

Tangohia te 1 i te 31, ka 30.

$$30+x-x^{2}=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-x^{2}+x+30=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx+30. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=-30=-30$$

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 -30.

$$-1,30 -2,15 -3,10 -5,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+30=29 -2+15=13 -3+10=7 -5+6=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=6 b=-5$$

Tuhia anō te -x^{2}+x+30 hei \left(-x^{2}+6x\right)+\left(-5x+30\right).

$$\left(-x^{2}+6x\right)+\left(-5x+30\right)$$

Tauwehea te -x i te tuatahi me te -5 i te rōpū tuarua.

$$-x\left(x-6\right)-5\left(x-6\right)$$

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

$$\left(x-6\right)\left(-x-5\right)$$

Hei kimi otinga whārite, me whakaoti te x-6=0 me te -x-5=0.

$$x=6 x=-5$$

Whakakapia te 6 mō te x i te whārite \sqrt{31-x}=x-1.

$$\sqrt{31-6}=6-1$$

Whakarūnātia. Ko te uara x=6 kua ngata te whārite.

$$5=5$$

Whakakapia te -5 mō te x i te whārite \sqrt{31-x}=x-1.

$$\sqrt{31-\left(-5\right)}=-5-1$$

Whakarūnātia. Ko te uara x=-5 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$6=-6$$

Ko te whārite \sqrt{31-x}=x-1 he rongoā ahurei.

$$x=6$$