Question

Biết a<b<0 và a.b\(\ne\)0 thỏa mãn pt: a(a+2)+b(b-2)-2ab=63. Tính b-a

Answer 1

\(\Leftrightarrow a^2+b^2-2ab+2a-2b=63\)

\(\Leftrightarrow\left(b-a\right)^2-2\left(b-a\right)-63=0 \)

\(\Leftrightarrow\left(b-a\right)^2-9\left(b-a\right)+7\left(b-a\right)-63=0\)

\(\Leftrightarrow\left(b-a\right)\left(b-a-9\right)+7\left(b-a-9\right)=0\)

\(\Leftrightarrow\left(b-a-9\right)\left(b-a+7\right)=0\)

\(\Leftrightarrow b-a-9=0\) hoặc \(b-a+7=0\)

\(\Leftrightarrow b-a=9\) hoặc \(b-a=-7\left(l\right)\) vì b > a