Question

If a/b=b/c=c/d show that a^3+b^3+c^3/ b^3+c^3+d^3= a/d​

Answer 1

Step-by-step explanation:

If a/b= b/c= c/d, can you prove that: (a^3+b^3+c^3) ÷ (b^3+c^3+d^3) =a/d?

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)

Putting c=ak^2 from eqn. (4) in eqn. (3),

d=ak^3…………………..(5)

To prove :- (a^3+b^3+c^3)/(b^3+c^3+d^3) = a/d

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)

=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)

= 1/(d/a)

=a/d. Proved.