Question

cho:\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}cm:\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)

 

Answer 1

\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{a+b+c}{b+c+d}\Rightarrow\left(\frac{a}{b}\right)^3=\left(\frac{b}{c}\right)^3=\left(\frac{c}{d}\right)^3=\left(\frac{a+b+c}{b+c+d}\right)^3\left(1\right)\)

\(\left(\frac{a}{b}\right)^3=\left(\frac{b}{c}\right)^3=\left(\frac{c}{d}\right)^3=\frac{a}{b}.\frac{b}{c}.\frac{c}{d}=\frac{a.b.c}{b.c.d}=\frac{a}{d}\left(2\right)\)

Từ \(\left(1\right)và\left(2\right)\Rightarrowđpcm\)

ko chắc

Answer 2

áp dụng tính chất của dãy tỉ số bằng nhau ta có

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

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

vậy (a+b+c/b+c+d)^3=a/d (đpcm)