Whakaoti i te sqrt{x+5}+sqrt{2x+8}=1

$$\sqrt { x + 5 } + \sqrt { 2 x + 8 } = 1$$

Whakaoti mō x

$$x=-4$$

Ngā Upane Otinga

Me tango \sqrt{2x+8} mai i ngā taha e rua o te whārite.

$$\sqrt{x+5}=1-\sqrt{2x+8}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x+5}\right)^{2}=\left(1-\sqrt{2x+8}\right)^{2}$$

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

$$x+5=\left(1-\sqrt{2x+8}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(1-\sqrt{2x+8}\right)^{2}.

$$x+5=1-2\sqrt{2x+8}+\left(\sqrt{2x+8}\right)^{2}$$

Tātaihia te \sqrt{2x+8} mā te pū o 2, kia riro ko 2x+8.

$$x+5=1-2\sqrt{2x+8}+2x+8$$

Tāpirihia te 1 ki te 8, ka 9.

$$x+5=9-2\sqrt{2x+8}+2x$$

Me tango 9+2x mai i ngā taha e rua o te whārite.

$$x+5-\left(9+2x\right)=-2\sqrt{2x+8}$$

Hei kimi i te tauaro o 9+2x, kimihia te tauaro o ia taurangi.

$$x+5-9-2x=-2\sqrt{2x+8}$$

Tangohia te 9 i te 5, ka -4.

$$x-4-2x=-2\sqrt{2x+8}$$

Pahekotia te x me -2x, ka -x.

$$-x-4=-2\sqrt{2x+8}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(-x-4\right)^{2}=\left(-2\sqrt{2x+8}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(-x-4\right)^{2}.

$$x^{2}+8x+16=\left(-2\sqrt{2x+8}\right)^{2}$$

Whakarohaina te \left(-2\sqrt{2x+8}\right)^{2}.

$$x^{2}+8x+16=\left(-2\right)^{2}\left(\sqrt{2x+8}\right)^{2}$$

Tātaihia te -2 mā te pū o 2, kia riro ko 4.

$$x^{2}+8x+16=4\left(\sqrt{2x+8}\right)^{2}$$

Tātaihia te \sqrt{2x+8} mā te pū o 2, kia riro ko 2x+8.

$$x^{2}+8x+16=4\left(2x+8\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te 2x+8.

$$x^{2}+8x+16=8x+32$$

Tangohia te 8x mai i ngā taha e rua.

$$x^{2}+8x+16-8x=32$$

Pahekotia te 8x me -8x, ka 0.

$$x^{2}+16=32$$

Tangohia te 32 mai i ngā taha e rua.

$$x^{2}+16-32=0$$

Tangohia te 32 i te 16, ka -16.

$$x^{2}-16=0$$

Whakaarohia te x^{2}-16. Tuhia anō te x^{2}-16 hei x^{2}-4^{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).

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

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

$$x=4 x=-4$$

Whakakapia te 4 mō te x i te whārite \sqrt{x+5}+\sqrt{2x+8}=1.

$$\sqrt{4+5}+\sqrt{2\times 4+8}=1$$

Whakarūnātia. Ko te uara x=4 kāore e ngata ana ki te whārite.

$$7=1$$

Whakakapia te -4 mō te x i te whārite \sqrt{x+5}+\sqrt{2x+8}=1.

$$\sqrt{-4+5}+\sqrt{2\left(-4\right)+8}=1$$

Whakarūnātia. Ko te uara x=-4 kua ngata te whārite.

$$1=1$$

Ko te whārite \sqrt{x+5}=-\sqrt{2x+8}+1 he rongoā ahurei.

$$x=-4$$