a) \(\left(5x-2\right)^2-\left(7-6x\right)^2=0\)
\(\Leftrightarrow\left(5x-2-7+6x\right)\left(5x-2+7-6x\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}11x-9=0\\-x+5=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{9}{11}\\x=5\end{cases}}}\)
b) \(\left(3x-1\right)^2+\left(5x+2\right)^2=x+5\)
\(\Leftrightarrow9x^2+6x+1+25x^2+20x+4=x+5\)
\(\Leftrightarrow34x^2+26x+5=x+5\)
\(\Leftrightarrow34x^2+25x=0\)
\(\Leftrightarrow x\left(34x+25\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\34x+25=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\frac{-25}{34}\end{cases}}}\)
c) Tự làm nốt
a) ( 5x - 2 )2 - ( 7 - 6x )2 = 0
<=> [ 5x - 2 - ( 7 - 6x ) ][ 5x - 2 + ( 7 - 6x ) ] = 0
<=> [ 5x - 2 - 7 + 6x ][ 5x - 2 + 7 - 6x ] = 0
<=> [ 11x - 9 ][ 5 - x ] = 0
<=> \(\orbr{\begin{cases}11x-9=0\\5-x=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{9}{11}\\x=5\end{cases}}\)
b) ( 3x - 1 )2 + ( 5x + 2 )2 = x + 5
<=> 9x2 - 6x + 1 + 25x2 + 20x + 4 = x + 5
<=> 34x2 + 14x + 5 = x + 5
<=> 34x2 + 14x + 5 - x - 5 = 0
<=> 34x2 + 13x = 0
<=> 13x( 34/13x + 1 ) = 0
<=> \(\orbr{\begin{cases}13x=0\\\frac{34}{13}x+1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=-\frac{13}{34}\end{cases}}\)
c) ( x - 2 )2 - ( 3 + 2x )2 = 20x - 4
<=> x2 - 4x + 4 - ( 4x2 + 12x + 9 ) = 20x - 4
<=> x2 - 4x + 4 - 4x2 - 12x - 9 - 20x + 4 = 0
<=> -3x2 - 36x - 1 = 0
=> Vô nghiệm ( bấm EQN ra nghiệm vô tỉ )
a, \(\left(5x-2\right)^2-\left(7-6x\right)^2=0\)
\(\Leftrightarrow25x^2-20x+4-49+84x-36x^2=0\)
\(\Leftrightarrow-11x^2+64x-45=0\)
\(\Leftrightarrow x\left(11x-9\right)-5\left(11x-9\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(11x-9\right)=0\Leftrightarrow\orbr{\begin{cases}x=5\\x=\frac{9}{11}\end{cases}}\)
