Question

If a, b, c are in continued proportion, prove that
a/c = 2a^2-5ab+7b^2/2b^2-5ab+7c^2​

Answer 1

Step-by-step explanation:

given

a/b =b/c =K

then

a=bk and b=ck

a = (ck)k = ck^2 and b= can

LHS = a/c=ck/c

=k^2

RHS =2a^2 -5ab+7b^2/2b^2-5bc+7c^2 = 2(ck^2)^2 -5(ck^2)ck+7(ck)^2/2(ck)^2-5(ck)c+7c^2

After solving this equation the answer will be k^2

LHS = RHS

HENCE PROVED