d: Ta có: \(\sqrt{x\sqrt{x}-7}=1\)

\(\Leftrightarrow x\sqrt{x}-7=1\)

\(\Leftrightarrow\left(\sqrt{x}\right)^3=8\)

\(\Leftrightarrow x=4\)

\(a,ĐK:x\ge\dfrac{1}{3}\\ PT\Leftrightarrow\left|x-3\right|=3x-1\\ \Leftrightarrow\left[{}\begin{matrix}x-3=3x-1\left(x\ge3\right)\\x-3=1-3x\left(x< 3\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\left(ktm\right)\\x=1\left(tm\right)\end{matrix}\right.\Leftrightarrow x=1\\ b,ĐK:x\in R\\ PT\Leftrightarrow\left|1-2x\right|=5\\ \Leftrightarrow\left[{}\begin{matrix}1-2x=5\left(x\le\dfrac{1}{2}\right)\\2x-1=5\left(x>\dfrac{1}{2}\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\left(tm\right)\\x=3\left(tm\right)\end{matrix}\right.\)

\(c,ĐK:x\ge0\\ PT\Leftrightarrow\left|6x-2\right|=x\\ \Leftrightarrow\left[{}\begin{matrix}6x-2=x\left(x\ge\dfrac{1}{3}\right)\\6x-2=-x\left(x< \dfrac{1}{3}\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{5}\left(tm\right)\\x=\dfrac{2}{7}\left(tm\right)\end{matrix}\right.\\ d,ĐK:x\ge\sqrt[3]{49}\\ PT\Leftrightarrow x\sqrt{x}-7=1\\ \Leftrightarrow\sqrt{x^3}=8\\ \Leftrightarrow x^3=64\Leftrightarrow x=4\left(tm\right)\)

\(e,ĐK:x\le2\\ PT\Leftrightarrow4\left(x^2+7\right)=\left(2-x\right)^2\\ \Leftrightarrow4x^2+28=4-4x+x^2\\ \Leftrightarrow3x^2+4x+24=0\\ \Delta'=2^2-24\cdot3=-68< 0\\ \Leftrightarrow x\in\varnothing\)

D A A A A

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7: \(\Leftrightarrow\dfrac{201-x}{99}+1+\dfrac{203-x}{97}+1+\dfrac{205-x}{95}+1=0\)

=>300-x=0

hay x=300

=>2x-4+11 chia hết cho x-2

=>\(x-2\in\left\{1;-1;11;-11\right\}\)

=>\(x\in\left\{3;1;13;-9\right\}\)

số hạng là:

(21,25-3,25):1,50+1=13(số hạng)

tổng là:

(3,25+21,25).13:2=159,25

Ta có: \(\left(2+4+6+...+2004\right)\cdot x=501396\)

\(\Leftrightarrow\frac{\left(2+2004\right)\cdot\left[\left(2004-2\right)\div2+1\right]}{2}\cdot x=501396\)

\(\Leftrightarrow\frac{2006\cdot1002}{2}\cdot x=501396\)

\(\Leftrightarrow1005006\cdot x=501396\)

\(\Rightarrow x=\frac{250698}{502503}\)