`a)\sqrt{x^2-2x}=\sqrt{2-3x}`
Điều kiện:`{(x^2-2x>=0),(2-3x>=0):}`
`<=>{(x(x-2)>=0),(3x<=2):}`
`<=>{([(x>=2),(x<=0):}),(x<=2/3):}`
`<=>x<=0`
Bình phương hai vế ta có:
`x^2-2x=2-3x`
`<=>x^2+x-2=0`
`a+b+c=1+1-2=0`
`<=>[(x_1=1(ktm)),(x_2=-2(tm)):}`
Vậy `S={-2}.`
`b)\sqrt{x-3}-2\sqrt{x^2-9}=0`
Điều kiện:`{(x-3>=0),(x^2-9>=0):}`
`<=>{(x-3>=0),((x-3)(x+3)>=0):}`
`<=>x-3>=0`
`<=>x>=3`
`pt<=>\sqrt{x-3}(1-2\sqrt{x+3})=0`
`**\sqrt{x-3}=0`
`<=>x-3=0`
`<=>x=3`
`**1-2\sqrt{x+3}=0`
`<=>2\sqrt{x+3}=1`
`<=>\sqrt{x+3}=1/2`
`<=>x+3=1/4`
`<=>x=-11/4(ktm)`
Vậy `S={3}.`
`c)1/2\sqrt{x-1}-3/2\sqrt{9x-9}+24\sqrt{(x-1)/64}=-17(x>=1)`
`<=>1/2\sqrt{x-1}-3/2*\sqrt{9(x-1)}+24*\sqrt{x-1}/8=-17`
`<=>-1/2\sqrt{x-1}-9/2\sqrt{x-1}+3\sqrt{x-1}=-17`
`<=>-2\sqrt{x-1}=-17`
`<=>\sqrt{x-1}=17/2`
`<=>x-1=289/4`
`<=>x=293/4(tm)`
Vậy `S={293/4}.`
`d)x+y+12=4\sqrt{x}+6\sqrt{y-1}(x>=0,y>=1)`
`<=>x-4\sqrtx+y-6sqrt{y-1}+12=0`
`<=>x-4sqrtx+4+y-1-6sqrt{x-1}+9=0`
`<=>(sqrtx-2)^2+(sqrt{y-1}-3)^2=0`
`<=>{(sqrtx-2=0),(sqrt{y-1}-3=0):}`
`<=>{(x=4),(y=10):}`
Vậy `(x,y)=(4,10).`
