Whakaoti i te z-1=sqrt{21-3z}

$$z - 1 = \sqrt { 21 - 3 z }$$

Whakaoti mō z

$$z=4$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(z-1\right)^{2}=\left(\sqrt{21-3z}\right)^{2}$$

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

$$z^{2}-2z+1=\left(\sqrt{21-3z}\right)^{2}$$

Tātaihia te \sqrt{21-3z} mā te pū o 2, kia riro ko 21-3z.

$$z^{2}-2z+1=21-3z$$

Tangohia te 21 mai i ngā taha e rua.

$$z^{2}-2z+1-21=-3z$$

Tangohia te 21 i te 1, ka -20.

$$z^{2}-2z-20=-3z$$

Me tāpiri te 3z ki ngā taha e rua.

$$z^{2}-2z-20+3z=0$$

Pahekotia te -2z me 3z, ka z.

$$z^{2}+z-20=0$$

Hei whakaoti i te whārite, whakatauwehea te z^{2}+z-20 mā te whakamahi i te tātai z^{2}+\left(a+b\right)z+ab=\left(z+a\right)\left(z+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=-20$$

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 -20.

$$-1,20 -2,10 -4,5$$

Tātaihia te tapeke mō ia takirua.

$$-1+20=19 -2+10=8 -4+5=1$$

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

$$a=-4 b=5$$

Me tuhi anō te kīanga whakatauwehe \left(z+a\right)\left(z+b\right) mā ngā uara i tātaihia.

$$\left(z-4\right)\left(z+5\right)$$

Hei kimi otinga whārite, me whakaoti te z-4=0 me te z+5=0.

$$z=4 z=-5$$

Whakakapia te 4 mō te z i te whārite z-1=\sqrt{21-3z}.

$$4-1=\sqrt{21-3\times 4}$$

Whakarūnātia. Ko te uara z=4 kua ngata te whārite.

$$3=3$$

Whakakapia te -5 mō te z i te whārite z-1=\sqrt{21-3z}.

$$-5-1=\sqrt{21-3\left(-5\right)}$$

Whakarūnātia. Ko te uara z=-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 z-1=\sqrt{21-3z} he rongoā ahurei.

$$z=4$$