Question

Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\). CMR :\(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)

Answer 1

đặt\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=k\)

=>a=bk

    b=ck

    c=dk

ta có:

\(\left(\frac{a+b+c}{b+c+d}\right)^3=\left(\frac{bk+ck+dk}{ck+dk+d}\right)^3=\left(\frac{ck^2+dk^2+dk}{dk^2+dk+d}\right)^3=\left(\frac{dk^3+dk^2+dk}{dk^2+dk+d}\right)^3=\left(\frac{dk\left(k^2+k+1\right)}{d\left(k^2+k+1\right)}\right)^3=k^3\)

\(\frac{a}{d}=\frac{bk}{d}=\frac{ck^2}{d}=\frac{dk^3}{d}=k^3\)

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

nhớ tick cho mình vs nha