d) ĐKXD:`x≥1`
`\sqrt{x+2\sqrt{x-1}}=2`
`⇔x+2\sqrt{x-1}=4`
`⇔2\sqrt{x-1}=4-x` (ĐKXD:`x≤4`)
`⇔4(x-1)=(4-x)^2`
`⇔4x-4=16-8x+x^2`
`⇔x^2-12x+20=0`
`⇔x^2-12x+36-16=0`
`⇔(x-6)^2=16`
`⇔`\(\left[ \begin{array}{l}x-6=4\\x-6=-4\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=10(KTM)\\x=2\end{array} \right.\)
e)ĐKXD: `x≥2`
`\sqrt{x-2\sqrt{x-1}}=\sqrt{x-1}-1`
`⇔x-2\sqrt{x-1}=x-1-2\sqrt{x-1}+1`
`⇔x=x`
`⇔x∈R`
Kết hợp ĐKXD:
`⇒x≥2`
f)ĐKXD: `x≤1/4`
`\sqrt{x^2-1/2x+1/16}=1/4-x`
`⇔\sqrt{(x-1/4)^2}=1/4-x`
`⇔|x-1/4|=1/4-x`
`⇔`Vô số nghiệm (do `x≤1/4`)
Kết hợp ĐKXD:
`⇒x≤1/4`
