Question

Giải phương trình:

\(\dfrac{\left(x-2\right)^2}{12}-\dfrac{\left(x+1\right)^2}{21}=\dfrac{\left(x-4\right)\left(x-6\right)}{28}\)

Answer 1

\(\dfrac{\left(x-2\right)^2}{12}-\dfrac{\left(x+1\right)^2}{21}=\dfrac{\left(x-4\right)\left(x-6\right)}{28}\)

\(\Leftrightarrow\dfrac{7\left(x-2\right)^2}{84}-\dfrac{4\left(x+1\right)^2}{84}=\dfrac{3\left(x-4\right)\left(x-6\right)}{84}\)

\(\Leftrightarrow7\left(x-2\right)^2-4\left(x+1\right)^2=3\left(x-4\right)\left(x-6\right)\)

\(\Leftrightarrow7\left(x^2-4x+4\right)-4\left(x^2+2x+1\right)=3\left(x^2-10x+24\right)\)

\(\Leftrightarrow7x^2-28x+28-4x^2-8x-4=3x^2-30x+72\)

\(\Leftrightarrow7x^2-4x^2-3x^2-28x-8x+30x+28-4-72=0\)

\(\Leftrightarrow-6x-48=0\)

\(\Leftrightarrow-6x=48\)

\(\Leftrightarrow x=8\)

Vậy tập nghiệm của pt là S = { 8 }