Question

bài 1: cho tỉ lệ thức a/b=c/d. CMR

a)a/3a+b=c/3c+d

b)(a-b)^2/(c-d)^2=a.b/c.d

c)2.a+3.b/2.a-3.b=2.c+3.d/2.c-3.d

Bài 2: Tìm x biết x=a/b+c=b/c+a=c/a+b

Answer 1

Bài 1: 
Đặt a/b=c/d=k

=>a=bk; c=dk

a: \(\dfrac{a}{3a+b}=\dfrac{bk}{3bk+b}=\dfrac{k}{3k+1}\)

\(\dfrac{c}{3c+d}=\dfrac{dk}{3dk+d}=\dfrac{k}{3k+1}\)

Do đó: \(\dfrac{a}{3a+b}=\dfrac{c}{3c+d}\)

c: \(\dfrac{2a+3b}{2a-3b}=\dfrac{2\cdot bk+3b}{2\cdot bk-3b}=\dfrac{2k+3}{2k-3}\)

\(\dfrac{2c+3d}{2c-3d}=\dfrac{2dk+3d}{2dk-3d}=\dfrac{2k+3}{2k-3}\)

Do đó: \(\dfrac{2a+3b}{2a-3b}=\dfrac{2c+3d}{2c-3d}\)