Question

Giải phương trình:

1. 5-(6-x)=4(3-2x)

2. (x+1)(x+9)=(x+3)(x+5)

3. \(\dfrac{3\left(5x-2\right)}{4}\) -2=\(\dfrac{7x}{3}\)-5(x-7)

4. 3(x+1)(2x+5)=3(x+1)(7x-4)

5. (x-2)²-(3x+1)²+x(4x-1)=0

Answer 1

2. \(\left(x+1\right)\left(x+9\right)=\left(x+3\right)\left(x+5\right)\)

\(\Leftrightarrow\)\(x^2+9x+x+9=x^2+5x+3x+15\)

\(\Leftrightarrow x^2+9x+x-x^2-5x-3x=15-9\)

\(\Leftrightarrow2x=6\)

\(\Leftrightarrow x=\dfrac{6}{2}\Rightarrow x=3\)

\(S=\left\{3\right\}\)

Answer 2

\(1,5-\left(6-x\right)=4\left(3-2x\right)\)

\(\Leftrightarrow5-6+x=12-8x\)

\(\Leftrightarrow x+8x=12-5+6\)

\(\Leftrightarrow9x=13\)

\(\Leftrightarrow x=\dfrac{13}{9}\)

Vậy tập nghiệm của pt là \(S=\left\{\dfrac{13}{9}\right\}\)

\(2,\left(x+1\right)\left(x+9\right)=\left(x+3\right)\left(x+5\right)\)

\(\Leftrightarrow x^2+10x+9=x^2+8x+15\)

\(\Leftrightarrow x^2+10x+9-x^2-8x-15=0\)

\(\Leftrightarrow2x-6=0\)

\(\Leftrightarrow x=3\)

Vậy tập nghiệm của pt là S = { 3 }

\(3,\dfrac{3\left(5x-2\right)}{4}-2=\dfrac{7x}{3}-5\left(x-7\right)\)

\(\Leftrightarrow\dfrac{9\left(5x-2\right)-24}{12}=\dfrac{28x-60\left(x-7\right)}{12}\)

\(\Rightarrow45x-18-24=28x-60x+420\)

\(\Leftrightarrow45x-28x+60x=420+18+24\)

\(\Leftrightarrow77x=462\)

\(\Leftrightarrow x=6\)

Vậy tập nghiệm của pt là S = { 6 }

\(4,3\left(x+1\right)\left(2x+5\right)=3\left(x+1\right)\left(7x-4\right)\)

\(\Leftrightarrow3\left(x+1\right)\left(2x+5\right)-3\left(x+1\right)\left(7x-4\right)=0\)

\(\Leftrightarrow3\left(x+1\right)\left(2x+5-7x+4\right)=0\)

\(\Leftrightarrow3\left(x+1\right)\left(-5x+9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\-5x+9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\dfrac{9}{5}\end{matrix}\right.\)

Vậy tập nghiệm của pt là \(S=\left\{-1;\dfrac{9}{5}\right\}\)

\(5,\left(x-2\right)^2-\left(3x+1\right)^2+x\left(4x-1\right)=0\)

\(\Leftrightarrow\left(x-2-3x-1\right)\left(x-2+3x+1\right)+x\left(4x-1\right)=0\)

\(\Leftrightarrow\left(-2x-3\right)\left(4x-1\right)+x\left(4x-1\right)=0\)

\(\Leftrightarrow\left(4x-1\right)\left(-2x-3+x\right)=0\)

\(\Leftrightarrow\left(4x-1\right)\left(-x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}4x-1=0\\-x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=-3\end{matrix}\right.\)

Vậy tập nghiệm của pt là \(S=\left\{\dfrac{1}{4};-3\right\}\)