Question

If a,b,c,d and e are in continued proportion prove that a:e=a^4:b^4

Answer 1

question:if a,b,c,d are in continued proportion, prove that:a:e=a power 4 :b power4.

solution:a,b,c,d,e are in continued proportion

=)a/b=b/c=c/a=a/c=t(say)

d=ek, c=ek square ,b=ek cube and a=ek4

now.L.H.S=ac

=ek4/e R.H.S A4/b4=k4

=(ek4)4/(ek3)4=e4k16/e4k12

=k16-12=k4

L.H.S=RH.S