Whakaoti i te v=sqrt{2v+15}

$$v = \sqrt { 2 v + 15 }$$

Whakaoti mō v

$$v=5$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$v^{2}=\left(\sqrt{2v+15}\right)^{2}$$

Tātaihia te \sqrt{2v+15} mā te pū o 2, kia riro ko 2v+15.

$$v^{2}=2v+15$$

Tangohia te 2v mai i ngā taha e rua.

$$v^{2}-2v=15$$

Tangohia te 15 mai i ngā taha e rua.

$$v^{2}-2v-15=0$$

Hei whakaoti i te whārite, whakatauwehea te v^{2}-2v-15 mā te whakamahi i te tātai v^{2}+\left(a+b\right)v+ab=\left(v+a\right)\left(v+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-2 ab=-15$$

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 -15.

$$1,-15 3,-5$$

Tātaihia te tapeke mō ia takirua.

$$1-15=-14 3-5=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -2.

$$a=-5 b=3$$

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

$$\left(v-5\right)\left(v+3\right)$$

Hei kimi otinga whārite, me whakaoti te v-5=0 me te v+3=0.

$$v=5 v=-3$$

Whakakapia te 5 mō te v i te whārite v=\sqrt{2v+15}.

$$5=\sqrt{2\times 5+15}$$

Whakarūnātia. Ko te uara v=5 kua ngata te whārite.

$$5=5$$

Whakakapia te -3 mō te v i te whārite v=\sqrt{2v+15}.

$$-3=\sqrt{2\left(-3\right)+15}$$

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

$$-3=3$$

Ko te whārite v=\sqrt{2v+15} he rongoā ahurei.

$$v=5$$