Datrys sqrt{x+6}-sqrt{9x+70}=-2sqrt{x+9}

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

Datrys ar gyfer x

$$x=-5$$

Camau Ateb

Sgwariwch ddwy ochr yr hafaliad.

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

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(\sqrt{x+6}-\sqrt{9x+70}\right)^{2}.

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

Cyfrifo \sqrt{x+6} i bŵer 2 a chael x+6.

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

Cyfrifo \sqrt{9x+70} i bŵer 2 a chael 9x+70.

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

Cyfuno x a 9x i gael 10x.

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

Adio 6 a 70 i gael 76.

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

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

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

Cyfrifo -2 i bŵer 2 a chael 4.

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

Cyfrifo \sqrt{x+9} i bŵer 2 a chael x+9.

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

Defnyddio’r briodwedd ddosbarthu i luosi 4 â x+9.

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

Tynnu 10x+76 o ddwy ochr yr hafaliad.

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

I ddod o hyd i wrthwyneb 10x+76, dewch o hyd i wrthwyneb pob term.

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

Cyfuno 4x a -10x i gael -6x.

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

Tynnu 76 o 36 i gael -40.

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

Sgwariwch ddwy ochr yr hafaliad.

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

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

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

Cyfrifo -2 i bŵer 2 a chael 4.

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

Cyfrifo \sqrt{x+6} i bŵer 2 a chael x+6.

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

Cyfrifo \sqrt{9x+70} i bŵer 2 a chael 9x+70.

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

Defnyddio’r briodwedd ddosbarthu i luosi 4 â x+6.

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

Cyfrifwch y briodoledd ddosrannol drwy luosi pob 4x+24 gan bob 9x+70.

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

Cyfuno 280x a 216x i gael 496x.

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

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(-6x-40\right)^{2}.

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

Tynnu 36x^{2} o'r ddwy ochr.

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

Cyfuno 36x^{2} a -36x^{2} i gael 0.

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

Tynnu 480x o'r ddwy ochr.

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

Cyfuno 496x a -480x i gael 16x.

$$16x+1680=1600$$

Tynnu 1680 o'r ddwy ochr.

$$16x=1600-1680$$

Tynnu 1680 o 1600 i gael -80.

$$16x=-80$$

Rhannu’r ddwy ochr â 16.

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

Rhannu -80 â 16 i gael -5.

$$x=-5$$

Amnewid -5 am x yn yr hafaliad \sqrt{x+6}-\sqrt{9x+70}=-2\sqrt{x+9}.

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

Symleiddio. Mae'r gwerth x=-5 yn bodloni'r hafaliad.

$$-4=-4$$

Mae gan yr hafaliad \sqrt{x+6}-\sqrt{9x+70}=-2\sqrt{x+9} ateb unigryw.

$$x=-5$$