If a,b,c re in continued proportion then show that `a/c=(a^2+ab+b^2)/(b^2+bc+c^2)`

If a,b,c are in continued proportion, then prove that a/(a+2b)=(a-2b)/(a-4c)

If a,b,c are in continued proportion, then prove that (b/(b+c)=(a-b)/(a-c)

If a,b,c,d are in proportion, then prove that (a^2+ab+b^2)/(a^2-ab+b^2)=(c^2+cd+d^2)/(c^2-cd+d^2)

a,b,c are in continued proportion.If a=3 and c=27 then find b.

If a,b,c,d are in proportion, then prove that sqrt((a^2+5c^2)/(b^2+5d^2))=a/b

a, b, c are in continued proportion. If a =3and c = 27 then find b.

If a/b =b/c and a,b, c gt 0 , then prove that (a+b)^2/(b+c)^2 = (a^2 +b^2)/(b^2 +c^2)

If a/b=b/c and a,b,c>0 then show that, (a^2+b^2)(b^2+c^2)=(ab+bc)^2