1/

\(\frac{x-1}{13}-\frac{2x-13}{15}=\frac{3x-15}{27}-\frac{4x-27}{29}\)

\(\Leftrightarrow\left(\frac{x-1}{13}-1\right)-\left(\frac{2x-13}{15}-1\right)=\left(\frac{3x-15}{27}-1\right)-\left(\frac{4x-27}{29}-1\right)\)

\(\Leftrightarrow\frac{x-14}{13}-\frac{2\left(x-14\right)}{15}=\frac{3\left(x-14\right)}{27}-\frac{4\left(x-14\right)}{29}\)

\(\Leftrightarrow\frac{x-14}{13}-\frac{2\left(x-14\right)}{15}-\frac{3\left(x-14\right)}{27}+\frac{4\left(x-14\right)}{29}=0\)

\(\Leftrightarrow\left(x-14\right)\left(\frac{1}{13}-\frac{2}{15}-\frac{3}{27}+\frac{4}{29}\right)=0\)

\(\Leftrightarrow x-14=0\)(vì 1/13 -2/15 -3/27 +4/29 khác 0)

\(\Leftrightarrow x=14\)

vậy...................

2/ 

\(a,ĐKXĐ:x\ne\pm2\)

\(b,A=\frac{4}{3x-6}-\frac{x}{x^2-4}\)

          \(=\frac{4}{3\left(x-2\right)}-\frac{x}{\left(x-2\right)\left(x+2\right)}\)

           \(=\frac{4\left(x+2\right)-3x}{3\left(x-2\right)\left(x+2\right)}\)

            \(=\frac{x+8}{3\left(x-2\right)\left(x+2\right)}\)

c,với \(x\ne\pm2\)ta có \(A=\frac{x+8}{3\left(x-2\right)\left(x+2\right)}\)

với x=1 thay vào A ta có \(A=\frac{1+8}{3\left(1-2\right)\left(1+2\right)}=\frac{9}{-9}=-1\)

\(\left(x-1\right)^3-\left(x+3\right)\left(x^2-3x+9\right)=-3x\left(x+2\right)\)

\(\Leftrightarrow\left(x^3-3x^2+3x-1\right)-\left(x^3+27\right)=-3x^2-6x\)

\(\Leftrightarrow-3x^2+3x-28=-3x^2-6x\)

\(\Leftrightarrow3x-28=-6x\Leftrightarrow9x=28\)

\(\Leftrightarrow x=\frac{28}{9}\)

Vậy tập nghiệm S\(=\left\{\frac{28}{9}\right\}\)

Đáp án:

(x−1)3−(x+3)(x²−3x+9)=−3x(x+2)

⇒x3−3x²+3x−1−(x³+3³)=−3x²−6x

⇒x³−3x²+3x−1−x³−27+3x²+6x=0

⇒9x−28=0

⇒x=\(\frac{28}{9}\)

Vậyx=\(\frac{28}{9}\)

#Châu's ngốc

\(A=-2x^2+5x-8\)

\(=-2\left(x^2-\frac{5}{2}x\right)-8\)

\(=-2\left(x^2-2.x.\frac{5}{4}+\frac{25}{16}-\frac{25}{16}\right)-8\)

\(=-2\left(x-\frac{5}{4}\right)^2-\frac{39}{8}\)

Vì \(-2\left(x-\frac{5}{4}\right)^2\le0;\forall x\)

\(\Rightarrow-2\left(x-\frac{5}{4}\right)^2-\frac{39}{8}\le-\frac{39}{8};\forall x\)

Dấu "="xảy ra \(\Leftrightarrow\left(x-\frac{5}{4}\right)^2=0\)

                      \(\Leftrightarrow x=\frac{5}{4}\)

Vậy MAX \(A=\frac{-39}{8}\)\(\Leftrightarrow x=\frac{5}{4}\)

Các bạn giúp mk với ạ

Nooooooooooo giúp

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bn vào đi ~

\(3x^2+3y^2+4xy+2x-2y+2=0\)

\(\Leftrightarrow\left(2x^2+2y^2+4xy\right)+\left(x^2+2x+1\right)+\left(y^2-2y+1\right)=0\)

\(\Leftrightarrow2\left(x^2+y^2+2xy\right)+\left(x+1\right)^2+\left(y-1\right)^2=0\)

\(\Leftrightarrow2\left(x+y\right)^2+\left(x+1\right)^2+\left(y-1\right)^2=0\)

Vì \(\left(x+y\right)^2\ge0\); \(\left(x+1\right)^2\ge0\); \(\left(y-1\right)^2\ge0\)\(\forall x,y\)

\(\Rightarrow2\left(x+y\right)^2+\left(x+1\right)^2+\left(y-1\right)^2\ge0\)

Dấu " = " xảy ra \(\Leftrightarrow\hept{\begin{cases}x+y=0\\x+1=0\\y-1=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-y\\x=-1\\y=1\end{cases}}\)

Vậy \(x=-1\)và \(y=1\)