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\(\left(x+\frac{1}{2}\right)^3:3=-\frac{1}{81}\)

\(\Rightarrow\left(x +\frac{1}{2}\right)^3=-\frac{1}{27}\)

\(\Rightarrow\left(x+\frac{1}{2}\right)^3=\left(-\frac{1}{3}\right)^3\)

\(\Rightarrow x+\frac{1}{2}=-\frac{1}{3}\Leftrightarrow x=-\frac{1}{3}-\frac{1}{2}\Leftrightarrow x=-\frac{5}{6}\)

Vậy \(x=-\frac{5}{6}\)

\(6,\\ a,\\ 1,A=x^2+3x+7=\left(x+\dfrac{3}{2}\right)^2+\dfrac{19}{4}\ge\dfrac{19}{4}\)

Dấu \("="\Leftrightarrow x=-\dfrac{3}{2}\)

\(2,B=\left(x-2\right)\left(x-5\right)\left(x^2-7x+10\right)=\left(x-2\right)^2\left(x-5\right)^2\ge0\)

Dấu \("="\Leftrightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\)

\(b,\\ 1,A=11-10x-x^2=-\left(x+5\right)^2+36\le36\)

Dấu \("="\Leftrightarrow x=-5\)

cảm ơn nha:3

Ta có : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2016}\)

\(\Rightarrow2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2016}\)

\(\Rightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2016}\)

\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2015}{2016}\)

\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2015}{2016}\)

\(\Rightarrow1-\frac{2}{x+1}=\frac{2015}{2016}\)

\(\Rightarrow\frac{2}{x+1}=\frac{1}{2016}\)

=> x + 1 = 2016 . 2

=> x + 1 = 4032

=> x = 4031

Vậy x  = 4031

Câu 1: (2x-3)-(x-5)=(x+2)-(x-1)

2x -3 -x+5 = x+2 -x +1

2x -x -x +x = 2+1 +3 -5

x= 1

Câu 2:     2(x-1)-5(x+2)=10

2x -2 -5x -10 =10

2x -5x = 10 +2 +10

(2-5) x = 22

-3x= 22

x= 22/-3

Câu 1: ( 2x - 3 ) - ( x - 5 ) = ( x + 2 ) - ( x - 1 )
=> ( 2x - x ) - ( 3 - 5 ) = ( x - x ) + ( 2 + 1 )
=> x + 2 = 3
=> x = 1

Thử lại: ( 2 - 3 ) - ( 1 - 5 ) = ( 1 + 2 ) - ( 1 - 1 )
=> -1 + 4 = 3 - 0
=> 3 = 3    ( thoả mãn )

Câu 2: 2 ( x - 1 ) - 5 ( x + 2 ) = 10
=> ( 2x - 2 ) - ( 5x + 10 ) = 10
=> ( 2x - 5x ) - ( 2 + 10 ) = 10
=> -3x - 12 = 10
=> -3x = 22
=> x = ^-22/₃

Thử lại: 2 ( ^-22/₃ - 1 ) - 5 ( ^-22/₃ + 2 ) = 10
=> 2 * ^-25/₃ - 5 * ^-16/₃ = 10
=> ^-50/₃ - ^-80/₃ = 10
=> ^{(-50) - (-80)}/₃ = 10
=> 30 / 3 = 10    ( thoả mãn )