Question

If a/b=b/c=c/d, then b^3 + c^3+d^3 / a^3+b^3+c^3 will be ?​

Answer 1

$a/b=b/c=c/d= 1/k(let) \\ b=ak ,……(1) \\ c=bk. ……….(2) \\d=ck…………..(3) \\ Putting \: b=ak. \: from \: eqn. (1) \: in \: eqn. (2) \\ c=ak^2……….(4) \\ d=ak^3………………(5) \\ To \: prove :- (a^3+b^3+c^3)/(b^3+c^3+d^3) = a/d \\ </p><p>L.H.S.=(a^3+b^3+c^3)/(b^3+c^3+d^3) \\ Putting \: b=a.k…….(1). \\ \: c=a.k^2………..(4) \\ \: . and. \: d=a.k^3…………(5) \\ =(a^3+a^3.k^3+a^3.k^6)/(a^3.k^3+a^3.k^6+a^3.k^9) \\ </p><p>=a^3(1+k^3+k^6)a^3.k^3(1+k^3+k^6) \\ = 1/k^3 \\ Putting \: k^3= d/a \: from \: eqn. (5)</p><p>= 1/(d/a) \\ =a/d. Proved.$