a, \(\left|x-3,5\right|+\left|x-\frac{1}{3}\right|=0\)

\(\hept{\begin{cases}x-3,5\ge0\forall x\\x-\frac{1}{3}\ge0\forall x\end{cases}\Rightarrow\left|x-3,5\right|+\left|x-\frac{1}{3}\right|\ge0\forall x}\)

Dấu ''='' xảy ra <=> \(x-3,5=0\Leftrightarrow x=3,5\)

\(x-\frac{1}{3}=0\Leftrightarrow x=\frac{1}{3}\)

b, \(\left|x\right|+x=\frac{1}{3}\Leftrightarrow\left|x\right|=\frac{1}{3}-x\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{3}-x\\x=-\frac{1}{3}+x\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=\frac{1}{3}\\0\ne-\frac{1}{3}\end{cases}\Leftrightarrow}x=\frac{1}{6}}\)

c, \(\left|x-2\right|=x\Leftrightarrow\orbr{\begin{cases}x-2=x\\x-2=-x\end{cases}\Leftrightarrow\orbr{\begin{cases}-2\ne0\\x=1\end{cases}}}\)

d, tương tự c 

Sửa ý a) của bạn @akirafake 

a) \(\left|x-3,5\right|+\left|x-1,3\right|=0\)

Ta có : \(\left|x-3,5\right|+\left|x-1,3\right|=\left|-\left(x-3,5\right)\right|+\left|x-1,3\right|=\left|3,5-x\right|+\left|x-1,3\right|\)

Áp dụng BĐT \(\left|a\right|+\left|b\right|\ge\left|a+b\right|\)ta có :

\(\left|3,5-x\right|+\left|x-1,5\right|\ge\left|3,5-x+x-1,5\right|=\left|2\right|=2\)

mà \(\left|x-3,5\right|+\left|x-1,3\right|=0\)( vô lí )

Vậy không có giá trị của x thỏa mãn 

b) \(\left|x\right|+x=\frac{1}{3}\)

=> \(\left|x\right|=\frac{1}{3}-x\)

=> \(\orbr{\begin{cases}x=\frac{1}{3}-x\\x=x-\frac{1}{3}\end{cases}\Rightarrow}\orbr{\begin{cases}2x=\frac{1}{3}\\0x=-\frac{1}{3}\end{cases}\Rightarrow}2x=\frac{1}{3}\Rightarrow x=\frac{1}{6}\)

c) \(\left|x\right|-x=\frac{3}{4}\)

=> \(\left|x\right|=\frac{3}{4}+x\)

=> \(\orbr{\begin{cases}x=\frac{3}{4}+x\\x=-x-\frac{3}{4}\end{cases}\Rightarrow}\orbr{\begin{cases}0x=\frac{3}{4}\\2x=-\frac{3}{4}\end{cases}}\Rightarrow2x=-\frac{3}{4}\Rightarrow x=-\frac{3}{8}\)

d) \(\left|x-2\right|=x\)

=> \(\orbr{\begin{cases}x-2=x\\x-2=-x\end{cases}}\Rightarrow\orbr{\begin{cases}0x=2\\2x=2\end{cases}}\Rightarrow2x=2\Rightarrow x=1\)

e) \(\left|x+2\right|=x\)

=> \(\orbr{\begin{cases}x+2=x\\x+2=-x\end{cases}}\Rightarrow\orbr{\begin{cases}0x=-2\\2x=-2\end{cases}}\Rightarrow2x=-2\Rightarrow x=-1\)

Thế x = -1 ta được :

\(\left|-1+2\right|=-1\)( vô lí )

=> Không có giá trị của x thỏa mãn

a, ( x - 3 ) . ( x - 4 )  = 0              

=> x - 3 = 0 hoặc x - 4 = 0 

Nếu x - 3 = 0 => x = 3 

Nếu x - 4 = 0 => x = 4 

b, (\(\frac{1}{2}\)x  - 4 ) . ( x - \(\frac{1}{4}\)) = 0 

=>(  \(\frac{1}{2}\)x - 4 ) = 0    Hoặc  ( x - \(\frac{1}{4}\)) = 0 

Nếu ( \(\frac{1}{2}\)x - 4 ) = 0  => x = \(\frac{8}{1}\)

Nếu ( x - \(\frac{1}{4}\)) = 0     => x = \(\frac{1}{4}\)

c, (\(\frac{1}{3}\)- x ) . ( \(\frac{1}{2}\)+ 1 : x ) = 0 

=> ( \(\frac{1}{3}\)- x ) = 0 Hoặc ( \(\frac{1}{2}\)+ 1 : x ) = 0

Nếu (\(\frac{1}{3}\)- x ) = 0 => x = \(\frac{1}{3}\)

Nếu ( \(\frac{1}{2}\)+ 1 : x ) = 0 => x = \(\frac{-2}{1}\)

d, ( x + 3 ) . (  x - 4 ) + 2.(x + 3 ) = 0

=> (X + 3 ) = 0 Hoặc  ( x - 4 ) = 0 Hoặc 2. ( x + 3 ) = 0

Nếu x + 3 = 0 => x = 0

Nếu ( x - 4 ) = 0 => x = 4 

Nếu 2.(x + 3) = 0  => x = 3 

# Cụ MAIZ 

a. ( x - 3 ) ( x - 4 ) = 0

<=> \(\orbr{\begin{cases}x-3=0\\x-4=0\end{cases}}\)

<=> \(\orbr{\begin{cases}x=3\\x=4\end{cases}}\)

b. \(\left(\frac{1}{2}x-4\right)\left(x-\frac{1}{4}\right)=0\)

<=> \(\orbr{\begin{cases}\frac{1}{2}x-4=0\\x-\frac{1}{4}=0\end{cases}}\)

<=> \(\orbr{\begin{cases}x=8\\x=\frac{1}{4}\end{cases}}\)

                          Bài làm :

\(a\text{)}...\Leftrightarrow\orbr{\begin{cases}x-3=0\\x-4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=4\end{cases}}\)

\(b\text{)}...\Leftrightarrow\orbr{\begin{cases}\frac{1}{2}x-4=0\\x-\frac{1}{4}=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}\frac{1}{2}x=4\\x=0+\frac{1}{4}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=8\\x=\frac{1}{4}\end{cases}}\)

\(c\text{)}...\Leftrightarrow\orbr{\begin{cases}\frac{1}{3}-x=0\\\frac{1}{2}+1\div x=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{3}-0\\1\div x=-\frac{1}{2}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=-2\end{cases}}\)

\(d\text{)}...\Leftrightarrow\left(x+3\right)\left(x-4+2\right)=0\Leftrightarrow\left(x+3\right)\left(x-2\right)=0\Leftrightarrow\orbr{\begin{cases}x+3=0\\x-2=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-3\\x=2\end{cases}}\)

Bài làm :

\(a,\left(x-3\right)\left(x-4\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-3=0\\x-4=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=3\\x=4\end{cases}}\)

\(b,\left(\frac{1}{2}x-4\right)\left(x-\frac{1}{4}\right)=0\)

\(\Rightarrow\orbr{\begin{cases}\frac{1}{2}x-4=0\\x-\frac{1}{4}=0\end{cases}}\Rightarrow\orbr{\begin{cases}\frac{1}{2}x=4\\x=\frac{1}{4}\end{cases}}\Rightarrow\orbr{\begin{cases}x=8\\x=\frac{1}{4}\end{cases}}\)

\(c,\left(\frac{1}{3}-x\right).\left(\frac{1}{2}+1:x\right)=0\)

\(\Rightarrow\orbr{\begin{cases}\frac{1}{3}-x=0\\\frac{1}{2}+1:x=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=-2\end{cases}}\)

\(d,\left(x+3\right)\left(x-4\right)+2\left(x+3\right)=0\)

\(\Rightarrow\left(x+3\right)\left(x-4+2\right)=0\)

\(\Rightarrow\left(x+3\right)\left(x-2\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x+3=0\\x-2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-3\\x=2\end{cases}}\)

Học tốt nhé

          Bài làm :

\(a\text{)}...\Leftrightarrow\orbr{\begin{cases}x-3=0\\x-4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=4\end{cases}}\)

\(b\text{)}...\Leftrightarrow\orbr{\begin{cases}\frac{1}{2}x-4=0\\x-\frac{1}{4}=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}\frac{1}{2}x=4\\x=0+\frac{1}{4}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=8\\x=\frac{1}{4}\end{cases}}\)

\(c\text{)}...\Leftrightarrow\orbr{\begin{cases}\frac{1}{3}-x=0\\\frac{1}{2}+1\div x=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{3}-0\\1\div x=-\frac{1}{2}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=-2\end{cases}}\)

\(d\text{)}...\Leftrightarrow\left(x+3\right)\left(x-4+2\right)=0\Leftrightarrow\left(x+3\right)\left(x-2\right)=0\Leftrightarrow\orbr{\begin{cases}x+3=0\\x-2=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-3\\x=2\end{cases}}\)

ta có \(\frac{a}{b}< \frac{c}{d}=>ad< bc=>ady< bcy=>ady+abx< bcy+abx\)

\(=>a\left(bx+dy\right)< b\left(ãx+cy\right)=>\frac{a}{b}< \frac{xa+yc}{xb+yd}\left(1\right)\)

ta lại có tương tự \(adx+cdy< bcx+cdy\)

\(=>d\left(ax+cy\right)< c\left(bx+dy\right)=>\frac{xa+yc}{xb+yd}< \frac{c}{d}\left(2\right)\)

từ 1 and 2 => dpcm

\(\sqrt{x}=2=>x^2=4^2=16\)

trả lời 

Nếu \(\sqrt{x}=2\)thì \(x^2\)bằng :

A) 2 ; B) 4 ; C) 8 ; D) 16 .

hc tốt