Question

giải các phương trình sau :

a. (x-3)(x-4)-2.(3x-2)=\(\left(4-x\right)^2\)

b. \(\left(x+2\right)\left(x-2\right)+5x^2=\left(3x+1\right)-3x^2\)

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

d.\(\frac{3-x}{2018}+\frac{x-1}{2020}=\frac{-x}{2021}+1\)

Answer 1

a) Ta có: \(\left(x-3\right)\left(x-4\right)-2\left(3x-2\right)=\left(4-x\right)^2\)

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

\(\Leftrightarrow\left(x-4\right)\left[\left(x-3\right)-\left(x-4\right)\right]-2\left(3x-2\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(x-3-x+4\right)-6x+4=0\)

\(\Leftrightarrow x-4-6x+4=0\)

\(\Leftrightarrow-5x=0\)

mà -5<0

nên x=0

Vậy: x=0