Whakaoti i te p-4sqrt{p}=21

$$p - 4 \sqrt { p } = 21$$

Whakaoti mō p

$$p=49$$

Ngā Upane Otinga

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

$$-4\sqrt{p}=21-p$$

Pūruatia ngā taha e rua o te whārite.

$$\left(-4\sqrt{p}\right)^{2}=\left(21-p\right)^{2}$$

Whakarohaina te \left(-4\sqrt{p}\right)^{2}.

$$\left(-4\right)^{2}\left(\sqrt{p}\right)^{2}=\left(21-p\right)^{2}$$

Tātaihia te -4 mā te pū o 2, kia riro ko 16.

$$16\left(\sqrt{p}\right)^{2}=\left(21-p\right)^{2}$$

Tātaihia te \sqrt{p} mā te pū o 2, kia riro ko p.

$$16p=\left(21-p\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(21-p\right)^{2}.

$$16p=441-42p+p^{2}$$

Tangohia te 441 mai i ngā taha e rua.

$$16p-441=-42p+p^{2}$$

Me tāpiri te 42p ki ngā taha e rua.

$$16p-441+42p=p^{2}$$

Pahekotia te 16p me 42p, ka 58p.

$$58p-441=p^{2}$$

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

$$58p-441-p^{2}=0$$

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

$$-p^{2}+58p-441=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -p^{2}+ap+bp-441. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=58 ab=-\left(-441\right)=441$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 441.

$$1,441 3,147 7,63 9,49 21,21$$

Tātaihia te tapeke mō ia takirua.

$$1+441=442 3+147=150 7+63=70 9+49=58 21+21=42$$

Ko te otinga te takirua ka hoatu i te tapeke 58.

$$a=49 b=9$$

Tuhia anō te -p^{2}+58p-441 hei \left(-p^{2}+49p\right)+\left(9p-441\right).

$$\left(-p^{2}+49p\right)+\left(9p-441\right)$$

Tauwehea te -p i te tuatahi me te 9 i te rōpū tuarua.

$$-p\left(p-49\right)+9\left(p-49\right)$$

Whakatauwehea atu te kīanga pātahi p-49 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(p-49\right)\left(-p+9\right)$$

Hei kimi otinga whārite, me whakaoti te p-49=0 me te -p+9=0.

$$p=49 p=9$$

Whakakapia te 49 mō te p i te whārite p-4\sqrt{p}=21.

$$49-4\sqrt{49}=21$$

Whakarūnātia. Ko te uara p=49 kua ngata te whārite.

$$21=21$$

Whakakapia te 9 mō te p i te whārite p-4\sqrt{p}=21.

$$9-4\sqrt{9}=21$$

Whakarūnātia. Ko te uara p=9 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-3=21$$

Ko te whārite -4\sqrt{p}=21-p he rongoā ahurei.

$$p=49$$