Question

Cho a/b=b/c=c/d và b+c+d khác 0

CMR: (a+b+c/b+c+d)³ = a/d

Answer 1

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

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

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

Answer 2

(a/b)³=a/b.a/b.a/b=a.b.c/b.c.d=a/d(1)

(a/b)³=(b/c)³=(c/d)³=(a+b+c/b+c+d)³(2)

Từ (1) (2) = >đpcm