Đáp án + Giải thích các bước giải:
`a.`
`sqrt(4x+12)+sqrt(x+3)-1/4sqrt(16x+48)=6` `(x>= -3)`
`<=>sqrt(4(x+3))+sqrt(x+3)-1/4sqrt(16(x+3))=6`
`<=>2sqrt(x+3)+sqrt(x+3)-sqrt(x+3)=6`
`<=>(2+1-1)sqrt(x+3)=6`
`<=>sqrt(x+3)=3`
`<=>x+3=9`
`<=>x=6(TM)`
Vậy `S={6}`
`b.`
`x-sqrtx-20=0` `(x>=0)`
`<=>x-5sqrtx+4sqrtx-20=0`
`<=>sqrtx(sqrtx-5)+4(sqrtx-5)=0`
`<=>(sqrtx-5)(sqrtx+4)=0`
`<=>`\(\left[ \begin{array}{l}\sqrt x=5\\\sqrt x=-4 &\text{(loại)}\end{array} \right.\)
`<=>x=25(TM)`
Vậy `S={25}`
`c.`
`sqrt(x^2-10x+25)=2x-2` `(x>=1)`
`<=>x^2-10x+25=(2x-2)^2`
`<=>x^2-10x+25=4x^2-8x+4`
`<=>3x^2+2x-21=0`
`<=>3x^2+9x-7x-21=0`
`<=>3x(x+3)-7(x+3)=0`
`<=>(x+3)(3x-7)=0`
`<=>`\(\left[ \begin{array}{l}x=-3 &\text{(loại)}\\x=\dfrac{7}{3}&(TM)\end{array} \right.\)
Vậy `S={7/3}`
