Cho a/b=(a+b+c)3/(b+c+d)3 = [(a+b+c)/(b+c+d)]3
Ap dung tinh chat day ti so bang nhau ta co :
a/b=b/c=c/d ta có
(a+b+c)/(b+c+d)= a/b=b/c=c/d (1)
Mặt khác a/b=b/c \(\Rightarrow\)a=b2/c (2)
c/d=b/c $\Rightarrow$\(\Rightarrow\)d=c2/b (3)
Ta có (2)/(3)=a/d= b3/c3
(a/d)=(b/c)3 (4)
Theo (1 ) thì (a+b+c)/(b+c+d)=b/c
Vay kết hợp (1) suy ra (a+b+c)3/(b+c+d)3=(a/d)
cho a/b = b/c = c/d = d/a va a + b + c + d khac 0. CMR: a= b= c= d.
cho \(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\) voi a; b; c khac 0 va c khac cong tru d . CMR \(\frac{a}{b}=\frac{c}{d}\)
Cho a/b=b/c=c/d va b+c+d khác 0.CMR a/d= (a+b+c)3/(b+c+d)3
Cho a+b+c+d khac 0 va a/b+c+d=b/a+c+d=c/a+b+d=d/a+b+c.
Tinh gia tri A= a+b/c+d + b+c/a+d + c+d/a+b + d+a/b+ch
cho a/b=b/c=c/d=d/a va a+b+c khac 0.
Tinh M = 2a-b/c+d + 2b-c/a+d + 2c-d/a+b + 2d-a/b+c
cho a = b + c va c = b + d / b - d ( b ; d khac 0 )
c/m : a / b = c / d
cho a, b, c, d khac 0 va thoa man
ac=b^2; bd=c^2
chung minh \(\frac{a^3+b^3+c^3}{b^3+c^3+d^3}=\frac{a}{d}\)
cho a,b,c,d la 4 so khac 0 thoa man b^2 =ac va c^2=bd.Cmr\(\frac{a^3+b^3+c^3}{b^3+c^3+d^3}\)=\(\frac{a}{b}\)
cho a/b= c/d (b,c,d khac 0; c-2d khac 0) CMR :(a-2b)^4/(c-2d)^4=a^4+2017b^4/c^4+2017d^4
