Whakaoti i te sqrt{-5n+14}=-n

$$\sqrt { - 5 n + 14 } = - n$$

Whakaoti mō n

$$n=-7$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{-5n+14}\right)^{2}=\left(-n\right)^{2}$$

Tātaihia te \sqrt{-5n+14} mā te pū o 2, kia riro ko -5n+14.

$$-5n+14=\left(-n\right)^{2}$$

Tātaihia te -n mā te pū o 2, kia riro ko n^{2}.

$$-5n+14=n^{2}$$

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

$$-5n+14-n^{2}=0$$

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

$$-n^{2}-5n+14=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -n^{2}+an+bn+14. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-5 ab=-14=-14$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -14.

$$1,-14 2,-7$$

Tātaihia te tapeke mō ia takirua.

$$1-14=-13 2-7=-5$$

Ko te otinga te takirua ka hoatu i te tapeke -5.

$$a=2 b=-7$$

Tuhia anō te -n^{2}-5n+14 hei \left(-n^{2}+2n\right)+\left(-7n+14\right).

$$\left(-n^{2}+2n\right)+\left(-7n+14\right)$$

Tauwehea te n i te tuatahi me te 7 i te rōpū tuarua.

$$n\left(-n+2\right)+7\left(-n+2\right)$$

Whakatauwehea atu te kīanga pātahi -n+2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-n+2\right)\left(n+7\right)$$

Hei kimi otinga whārite, me whakaoti te -n+2=0 me te n+7=0.

$$n=2 n=-7$$

Whakakapia te 2 mō te n i te whārite \sqrt{-5n+14}=-n.

$$\sqrt{-5\times 2+14}=-2$$

Whakarūnātia. Ko te uara n=2 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$2=-2$$

Whakakapia te -7 mō te n i te whārite \sqrt{-5n+14}=-n.

$$\sqrt{-5\left(-7\right)+14}=-\left(-7\right)$$

Whakarūnātia. Ko te uara n=-7 kua ngata te whārite.

$$7=7$$

Ko te whārite \sqrt{14-5n}=-n he rongoā ahurei.

$$n=-7$$