Question

Cho a/b =c/d CM: a) 5a+3b/5c+3d=5a-3b/5c-3d. b) a^2+b^2/c^2+d^2=(a+b/c+d)^2

Answer 1

Vt lại đề nhé (khó nhìn)

Cho \(\dfrac{a}{b}=\dfrac{c}{d}\)

Chứng minh : \(\dfrac{5a+3b}{5c+3d}=\dfrac{5a-3b}{5c-3d}\)

Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=x\Rightarrow a=bx;c=dx\)

Lần lượt thay vào các vế, ta được :

\(\dfrac{5a+3b}{5a-3b}=\dfrac{5.b.x+3b}{5.b.x+3b}=\dfrac{b\left(5x+3\right)}{b\left(5x+3\right)}=\dfrac{5x+3}{5x+3}\left(1\right)\)

\(\dfrac{5c-3d}{5c-3d}=\dfrac{5.d.x-3d}{5.d.x-3d}=\dfrac{d\left(5x-3\right)}{d\left(5x-3\right)}=\dfrac{5x-3}{5x-3}\left(2\right)\)

Từ \(\left(1\right)và\left(2\right)\)

\(\Rightarrow\dfrac{5a+3b}{5c+3d}=\dfrac{5a-3b}{5c-3d}\left(đpcm\right)\)