a)\(ĐK:-3\le x\le6\)

\(PT\Leftrightarrow\sqrt{x+3}+\sqrt{6-x}=3\)

\(\Leftrightarrow x+3+6-x+2\sqrt{\left(x+3\right)\left(6-x\right)}=9\)

\(\Leftrightarrow\sqrt{\left(x+3\right)\left(6-x\right)}=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=6\end{matrix}\right.\left(tm\right)\)

b/ ĐKXĐ: \(x\ge7\)

\(\sqrt{3x-2}=1+\sqrt{x-7}\)

\(\Leftrightarrow3x-2=x-6+2\sqrt{x-7}\)

\(\Leftrightarrow x+2=\sqrt{x-7}\)

\(\Leftrightarrow x^2+4x+4=x-7\)

\(\Leftrightarrow x^2+3x+11=0\) (vô nghiệm)

c/ ĐKXĐ: \(x\ge1;x\ne50\)

\(1-\sqrt{3x+1}=\sqrt{x-1}-7\)

\(\Leftrightarrow\sqrt{x-1}+\sqrt{3x+1}=8\)

\(\Leftrightarrow4x+2\sqrt{3x^2-2x-1}=64\)

\(\Leftrightarrow\sqrt{3x^2-2x-1}=32-2x\) (\(x\le16\))

\(\Leftrightarrow3x^2-2x-1=\left(32-2x\right)^2\)

a: ĐKXĐ: 2-|x-2|>=0

=>|x-2|<=2

=>-2<=x-2<=2

=>0<=x<=4

TH1: 0<=x<2

=>x-2<0

mà \(\sqrt{2-\left|x-2\right|}>=0\forall x\) thỏa mãn ĐKXĐ

nên \(\sqrt{2-\left|x-2\right|}\) >x-2 với mọi x thỏa mãn

=>NHận

=>0<=x<2

TH2: 2<=x<=4

\(\sqrt{2-\left|x-2\right|}>x-2\)

=>\(2-\left|x-2\right|\ge\left(x-2\right)^2\)

=>\(\left(x-2\right)^2\le2-\left(x-2\right)=2-x+2=4-x\)

=>\(x^2-4x+4\le4-x\)

=>\(x^2-3x\le0\)

=>x(x-3)<=0

=>0<=x<=3

=>2<=x<=3

Vậy: 0<=x<=3

b: \(x^2+3x+2\ge2\cdot\sqrt{x^2+3x+5}\)

=>\(x^2+3x+5-2\sqrt{x^2+3x+5}-3\ge0\)

=>\(\left(\sqrt{x^2+3x+5}-3\right)\left(\sqrt{x^2+3x+5}+1\right)>=0\)

=>\(\sqrt{x^2+3x+5}-3\ge0\)

=>\(\sqrt{x^2+3x+5}\ge3\)

=>\(x^2+3x+5\ge9\)

=>\(x^2+3x-4\ge0\)

=>(x+4)(x-1)>=0

=>x>=1 hoặc x<=-4

a)x=6

b)x=6

d)x=0.2

ĐKXĐ: z>0

pt<=> \(\frac{x^3+3x^2\sqrt[3]{3x-2}-12x+\sqrt{x}-\sqrt{x}-8}{x}=0\)

<=> \(x^3+3x^2\sqrt[3]{3x+2}-12x-8=0\)

<=> \(3x^2\sqrt[3]{3x-2}-6x^2+x^3-6x^2+12x-8=0\)

<=> \(3x^2\left(\sqrt[3]{3x-2}-2\right)+\left(x-2\right)^3=0\)

<=> \(3x^2\cdot\frac{3x-2-8}{\left(\sqrt[3]{3x-2}\right)^2+2\sqrt[3]{3x-2}+4}+\left(x-2\right)^3=0\)

<=> \(\left(x-2\right)\left(\frac{9x^2}{\left(\sqrt[3]{3x-2}\right)^2+2\sqrt[3]{3x-2}+4}+\left(x-2\right)^2\right)=0\)

<=> \(x=2\)( vì cái trong ngoặc thứ 2 luôn dương vs mọi x>0)

vậy x=2

Một bài làm rất hay !

Nhìn không đủ chán rồi không dám động vào

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