Whakaoti i te p-1=sqrt{50-2p}

$$p - 1 = \sqrt { 50 - 2 p }$$

Whakaoti mō p

$$p=7$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(p-1\right)^{2}=\left(\sqrt{50-2p}\right)^{2}$$

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

$$p^{2}-2p+1=\left(\sqrt{50-2p}\right)^{2}$$

Tātaihia te \sqrt{50-2p} mā te pū o 2, kia riro ko 50-2p.

$$p^{2}-2p+1=50-2p$$

Tangohia te 50 mai i ngā taha e rua.

$$p^{2}-2p+1-50=-2p$$

Tangohia te 50 i te 1, ka -49.

$$p^{2}-2p-49=-2p$$

Me tāpiri te 2p ki ngā taha e rua.

$$p^{2}-2p-49+2p=0$$

Pahekotia te -2p me 2p, ka 0.

$$p^{2}-49=0$$

Whakaarohia te p^{2}-49. Tuhia anō te p^{2}-49 hei p^{2}-7^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(p-7\right)\left(p+7\right)=0$$

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

$$p=7 p=-7$$

Whakakapia te 7 mō te p i te whārite p-1=\sqrt{50-2p}.

$$7-1=\sqrt{50-2\times 7}$$

Whakarūnātia. Ko te uara p=7 kua ngata te whārite.

$$6=6$$

Whakakapia te -7 mō te p i te whārite p-1=\sqrt{50-2p}.

$$-7-1=\sqrt{50-2\left(-7\right)}$$

Whakarūnātia. Ko te uara p=-7 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-8=8$$

Ko te whārite p-1=\sqrt{50-2p} he rongoā ahurei.

$$p=7$$