Question

cho biết (a+b+c+1) (a-b-c+1)= (a-b+c-1) (a+b-c-1).chứng minh rằng a=bc

Answer 1

Ta có \(\left(a+b+c+1\right)\left(a-b-c+1\right)=\left(a-b+c-1\right)\left(a+b-c-1\right)\)

\(\Leftrightarrow\left[\left(a+1\right)+\left(b+c\right)\right]\left[\left(a+1\right)-\left(b+c\right)\right]=\left[\left(a-1\right)-\left(b-c\right)\right]\left[\left(a-1\right)+\left(b-c\right)\right]\)

\(\Leftrightarrow\left(a+1\right)^2-\left(b+c\right)^2=\left(a-1\right)^2-\left(b-c\right)^2\)

\(\Leftrightarrow a^2+2a+1-b^2-2bc-c^2=a^2-2a+1-b^2+2bc-c^2\)

\(\Leftrightarrow4a=4bc\Leftrightarrow a=bc\left(đpcm\right)\)