Lời giải:
Áp dụng TCDTSBN:
$\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{a+b+c}{b+c+d}$
$\Rightarrow \frac{a+b+c}{b+c+d}.\frac{a+b+c}{b+c+d}.\frac{a+b+c}{b+c+d}=\frac{a}{b}.\frac{b}{c}.\frac{c}{d}$
Hay $(\frac{a+b+c}{b+c+d})^3=\frac{a}{d}$ (đpcm)
1, Cho a/b = c/d . C/m (a+b/c+d)^2=a^2+b^2/c^2+d^2 ?
2, Cho (a+b+c+d)(a-b-c+d)=(a-b+c-d)(a+b-c-d)
C/m a/b=c/d ?
C/M:(a+b+c/b+c+d)^3=a/d
cho a/b=b/c=c/d
cho : a/b+c+d = b/ c+d+a = c/d+a+b = d/a+b+c
tính : M = a+b/c+d = b+c/d+a= c+d/a+b = d+a/b+c
cho a/b+c+d=b/c+d+a=c/d+a+b=d/b+c+a
tính M = (a+b/c+d)+(b+c/a+d)+(c+d/a+b)+(d+a/b+c)
cho 2016a+b+c+d/a=a+2016b+c+d/b=a+b+2016c+d/c=a+b+c+2016d/d tính M=a+b/c+d + c+d/d+a + c+d/a+b + d+a/b+c
Cho a, b, c, d thỏa mãn : b+c+d/a=a+c+d/b=a+b+d/c=a+b+c/d
Tính M= a/b+c+d + b/a+c+d + c/a+b+d + d/a+b+c
cho: 2a+b+c+d/a=a+2b+c+d/b=a+b+2c+d/c=a+b+c+2d/d.Tính M=a+b/c+d + b+c/d+a + c+d/a+b + d+a/b+c
cho các số a, b,c,d sao cho a+b+c/a = a+b+d/c= a+c+d/b= c+b+d/a
Tính giá trị biểu thức dưới đây M= d/a+b+c=c/a+b+d= b/a+c+d=a/c+b+d
Cho : 2*a+b+c+d/a =a+2*b+c+d/b =a+b+2*c+d/c =a+b+c+2*d/d . Tính M=a+b/c+d -b-c/d+a +c+d/a+d*d+a/b+c .Giúp mình với!
