Question

If a,b and c are in a.p than find (a-c)^2/b^2-ac

Answer 1

If a,b,c are CONSECUTIVE terms of an AP then
b=½(a+c) then b²=¼(a+c)²
(a-c)²/(b²-ac)
=(a-c)²/( ¼(a+c)²-ac)
=(a-c)²/[¼[(a+c)²-4ac]
=4(a-c)²/[a²-2ac+c²]
=4(a-c)²/(a-c)²
=4
This assumes that a and c are unequal.