Whakaoti i te sqrt{x+6}-sqrt{9x+70}=-2sqrt{x+9}

$$\sqrt { x + 6 } - \sqrt { 9 x + 70 } = - 2 \sqrt { x + 9 }$$

Whakaoti mō x

$$x=-5$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x+6}-\sqrt{9x+70}\right)^{2}=\left(-2\sqrt{x+9}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{x+6}-\sqrt{9x+70}\right)^{2}.

$$\left(\sqrt{x+6}\right)^{2}-2\sqrt{x+6}\sqrt{9x+70}+\left(\sqrt{9x+70}\right)^{2}=\left(-2\sqrt{x+9}\right)^{2}$$

Tātaihia te \sqrt{x+6} mā te pū o 2, kia riro ko x+6.

$$x+6-2\sqrt{x+6}\sqrt{9x+70}+\left(\sqrt{9x+70}\right)^{2}=\left(-2\sqrt{x+9}\right)^{2}$$

Tātaihia te \sqrt{9x+70} mā te pū o 2, kia riro ko 9x+70.

$$x+6-2\sqrt{x+6}\sqrt{9x+70}+9x+70=\left(-2\sqrt{x+9}\right)^{2}$$

Pahekotia te x me 9x, ka 10x.

$$10x+6-2\sqrt{x+6}\sqrt{9x+70}+70=\left(-2\sqrt{x+9}\right)^{2}$$

Tāpirihia te 6 ki te 70, ka 76.

$$10x+76-2\sqrt{x+6}\sqrt{9x+70}=\left(-2\sqrt{x+9}\right)^{2}$$

Whakarohaina te \left(-2\sqrt{x+9}\right)^{2}.

$$10x+76-2\sqrt{x+6}\sqrt{9x+70}=\left(-2\right)^{2}\left(\sqrt{x+9}\right)^{2}$$

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

$$10x+76-2\sqrt{x+6}\sqrt{9x+70}=4\left(\sqrt{x+9}\right)^{2}$$

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

$$10x+76-2\sqrt{x+6}\sqrt{9x+70}=4\left(x+9\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x+9.

$$10x+76-2\sqrt{x+6}\sqrt{9x+70}=4x+36$$

Me tango 10x+76 mai i ngā taha e rua o te whārite.

$$-2\sqrt{x+6}\sqrt{9x+70}=4x+36-\left(10x+76\right)$$

Hei kimi i te tauaro o 10x+76, kimihia te tauaro o ia taurangi.

$$-2\sqrt{x+6}\sqrt{9x+70}=4x+36-10x-76$$

Pahekotia te 4x me -10x, ka -6x.

$$-2\sqrt{x+6}\sqrt{9x+70}=-6x+36-76$$

Tangohia te 76 i te 36, ka -40.

$$-2\sqrt{x+6}\sqrt{9x+70}=-6x-40$$

Pūruatia ngā taha e rua o te whārite.

$$\left(-2\sqrt{x+6}\sqrt{9x+70}\right)^{2}=\left(-6x-40\right)^{2}$$

Whakarohaina te \left(-2\sqrt{x+6}\sqrt{9x+70}\right)^{2}.

$$\left(-2\right)^{2}\left(\sqrt{x+6}\right)^{2}\left(\sqrt{9x+70}\right)^{2}=\left(-6x-40\right)^{2}$$

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

$$4\left(\sqrt{x+6}\right)^{2}\left(\sqrt{9x+70}\right)^{2}=\left(-6x-40\right)^{2}$$

Tātaihia te \sqrt{x+6} mā te pū o 2, kia riro ko x+6.

$$4\left(x+6\right)\left(\sqrt{9x+70}\right)^{2}=\left(-6x-40\right)^{2}$$

Tātaihia te \sqrt{9x+70} mā te pū o 2, kia riro ko 9x+70.

$$4\left(x+6\right)\left(9x+70\right)=\left(-6x-40\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x+6.

$$\left(4x+24\right)\left(9x+70\right)=\left(-6x-40\right)^{2}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 4x+24 ki ia tau o 9x+70.

$$36x^{2}+280x+216x+1680=\left(-6x-40\right)^{2}$$

Pahekotia te 280x me 216x, ka 496x.

$$36x^{2}+496x+1680=\left(-6x-40\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(-6x-40\right)^{2}.

$$36x^{2}+496x+1680=36x^{2}+480x+1600$$

Tangohia te 36x^{2} mai i ngā taha e rua.

$$36x^{2}+496x+1680-36x^{2}=480x+1600$$

Pahekotia te 36x^{2} me -36x^{2}, ka 0.

$$496x+1680=480x+1600$$

Tangohia te 480x mai i ngā taha e rua.

$$496x+1680-480x=1600$$

Pahekotia te 496x me -480x, ka 16x.

$$16x+1680=1600$$

Tangohia te 1680 mai i ngā taha e rua.

$$16x=1600-1680$$

Tangohia te 1680 i te 1600, ka -80.

$$16x=-80$$

Whakawehea ngā taha e rua ki te 16.

$$x=\frac{-80}{16}$$

Whakawehea te -80 ki te 16, kia riro ko -5.

$$x=-5$$

Whakakapia te -5 mō te x i te whārite \sqrt{x+6}-\sqrt{9x+70}=-2\sqrt{x+9}.

$$\sqrt{-5+6}-\sqrt{9\left(-5\right)+70}=-2\sqrt{-5+9}$$

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

$$-4=-4$$

Ko te whārite \sqrt{x+6}-\sqrt{9x+70}=-2\sqrt{x+9} he rongoā ahurei.

$$x=-5$$