Question

Prove that equation sec^2x = 4ab/(a+b)^2 is only possible when a=b​

Answer 1

Answer:

we know

sec^2 x > = 1

if sec^2 x = 4ab/(a+b)^2.. then 4ab/(a+b)^2 >= 1

as (a+b)^2 > 0 so 4ab >= (a+b)^2 or 0 >= (a+b)^2 - 4ab or 0 >= (a-b)^2

as 0 <= (a-b)^2 so above is true if 0 = (a-b)^2 or a = b

so above is true only if a= b