Whakaoti i te sqrt{-2w+43}=w-4

$$\sqrt { - 2 w + 43 } = w - 4$$

Whakaoti mō w

$$w=9$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{-2w+43}\right)^{2}=\left(w-4\right)^{2}$$

Tātaihia te \sqrt{-2w+43} mā te pū o 2, kia riro ko -2w+43.

$$-2w+43=\left(w-4\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(w-4\right)^{2}.

$$-2w+43=w^{2}-8w+16$$

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

$$-2w+43-w^{2}=-8w+16$$

Me tāpiri te 8w ki ngā taha e rua.

$$-2w+43-w^{2}+8w=16$$

Pahekotia te -2w me 8w, ka 6w.

$$6w+43-w^{2}=16$$

Tangohia te 16 mai i ngā taha e rua.

$$6w+43-w^{2}-16=0$$

Tangohia te 16 i te 43, ka 27.

$$6w+27-w^{2}=0$$

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

$$-w^{2}+6w+27=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -w^{2}+aw+bw+27. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=-27=-27$$

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 -27.

$$-1,27 -3,9$$

Tātaihia te tapeke mō ia takirua.

$$-1+27=26 -3+9=6$$

Ko te otinga te takirua ka hoatu i te tapeke 6.

$$a=9 b=-3$$

Tuhia anō te -w^{2}+6w+27 hei \left(-w^{2}+9w\right)+\left(-3w+27\right).

$$\left(-w^{2}+9w\right)+\left(-3w+27\right)$$

Tauwehea te -w i te tuatahi me te -3 i te rōpū tuarua.

$$-w\left(w-9\right)-3\left(w-9\right)$$

Whakatauwehea atu te kīanga pātahi w-9 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(w-9\right)\left(-w-3\right)$$

Hei kimi otinga whārite, me whakaoti te w-9=0 me te -w-3=0.

$$w=9 w=-3$$

Whakakapia te 9 mō te w i te whārite \sqrt{-2w+43}=w-4.

$$\sqrt{-2\times 9+43}=9-4$$

Whakarūnātia. Ko te uara w=9 kua ngata te whārite.

$$5=5$$

Whakakapia te -3 mō te w i te whārite \sqrt{-2w+43}=w-4.

$$\sqrt{-2\left(-3\right)+43}=-3-4$$

Whakarūnātia. Ko te uara w=-3 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$7=-7$$

Ko te whārite \sqrt{43-2w}=w-4 he rongoā ahurei.

$$w=9$$