Whakaoti i te sqrt{5x+9}=2x+3

$$\sqrt { 5 x + 9 } = 2 x + 3$$

Whakaoti mō x

$$x=0$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{5x+9}\right)^{2}=\left(2x+3\right)^{2}$$

Tātaihia te \sqrt{5x+9} mā te pū o 2, kia riro ko 5x+9.

$$5x+9=\left(2x+3\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+3\right)^{2}.

$$5x+9=4x^{2}+12x+9$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$5x+9-4x^{2}=12x+9$$

Tangohia te 12x mai i ngā taha e rua.

$$5x+9-4x^{2}-12x=9$$

Pahekotia te 5x me -12x, ka -7x.

$$-7x+9-4x^{2}=9$$

Tangohia te 9 mai i ngā taha e rua.

$$-7x+9-4x^{2}-9=0$$

Tangohia te 9 i te 9, ka 0.

$$-7x-4x^{2}=0$$

Tauwehea te x.

$$x\left(-7-4x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -7-4x=0.

$$x=0 x=-\frac{7}{4}$$

Whakakapia te 0 mō te x i te whārite \sqrt{5x+9}=2x+3.

$$\sqrt{5\times 0+9}=2\times 0+3$$

Whakarūnātia. Ko te uara x=0 kua ngata te whārite.

$$3=3$$

Whakakapia te -\frac{7}{4} mō te x i te whārite \sqrt{5x+9}=2x+3.

$$\sqrt{5\left(-\frac{7}{4}\right)+9}=2\left(-\frac{7}{4}\right)+3$$

Whakarūnātia. Ko te uara x=-\frac{7}{4} kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$\frac{1}{2}=-\frac{1}{2}$$

Ko te whārite \sqrt{5x+9}=2x+3 he rongoā ahurei.

$$x=0$$