Whakaoti i te x=sqrt{11x-30}

$$x = \sqrt { 11 x - 30 }$$

Whakaoti mō x

$$x=6$$

$$x=5$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$x^{2}=\left(\sqrt{11x-30}\right)^{2}$$

Tātaihia te \sqrt{11x-30} mā te pū o 2, kia riro ko 11x-30.

$$x^{2}=11x-30$$

Tangohia te 11x mai i ngā taha e rua.

$$x^{2}-11x=-30$$

Me tāpiri te 30 ki ngā taha e rua.

$$x^{2}-11x+30=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}-11x+30 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-11 ab=30$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 30.

$$-1,-30 -2,-15 -3,-10 -5,-6$$

Tātaihia te tapeke mō ia takirua.

$$-1-30=-31 -2-15=-17 -3-10=-13 -5-6=-11$$

Ko te otinga te takirua ka hoatu i te tapeke -11.

$$a=-6 b=-5$$

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

$$\left(x-6\right)\left(x-5\right)$$

Hei kimi otinga whārite, me whakaoti te x-6=0 me te x-5=0.

$$x=6 x=5$$

Whakakapia te 6 mō te x i te whārite x=\sqrt{11x-30}.

$$6=\sqrt{11\times 6-30}$$

Whakarūnātia. Ko te uara x=6 kua ngata te whārite.

$$6=6$$

Whakakapia te 5 mō te x i te whārite x=\sqrt{11x-30}.

$$5=\sqrt{11\times 5-30}$$

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

$$5=5$$

Rārangihia ngā rongoā katoa o x=\sqrt{11x-30}.

$$x=6 x=5$$