Question

Cho \(a^2-b^2=4c^2\)

Chứng minh \(\left(5a-3b+8c\right).\left(5a-3b-8c\right)=\left(3a-5b\right)^2\)

Nhanh nhaaaa

Answer 1

ta có : \(\left(5a-3b+8c\right)\left(5a-3b-8c\right)=\left(3a-5b\right)^2\)

\(\Leftrightarrow\left(5a-3b\right)^2-\left(8c\right)^2=\left(3a-5b^2\right)\)

\(\Leftrightarrow\left(5a-3b\right)^2-\left(3a-5b\right)^2=\left(8c\right)^2\)

\(\Leftrightarrow\left(5a-3b-3a+5b\right)\left(5a-3b+3a-5b\right)=\left(8c\right)^2\)

\(\Leftrightarrow\left(2a+2b\right)\left(8a-8b\right)=64c^2\)

\(\Leftrightarrow16\left(a^2-b^2\right)=64c^2\Leftrightarrow a^2-b^2=4c^2\) đúng như giả thiết

\(\Rightarrow\left(đpcm\right)\)