Question

Cho a/b=b/c=c/d.Chứng minh rằng (a+b+c/b+c+d)^3=a/d

Answer 1

Ta có tính chất dãy tỉ 

a/b = b/c = c/d = a+b+c/b+c+d

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

=>  (a+b+c/b+c+d)³=a/b.b/c.c/d

=>  (a+b+c/b+c+d)³= a/d (đpcm)

Answer 2

Ta có tính chất dãy tỉ 

a/b = b/c = c/d = a+b+c/b+c+d

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

=>  (a+b+c/b+c+d)³=a/b.b/c.c/d

=>  (a+b+c/b+c+d)³= a/d (đpcm)