What is the minimum value of a^2 x+b^2 y where x y=c^2 ?

Step-by-step solution

Let p = a ^2 x + b ^2 y and xy = c ^2 y= c^2 x ...(1) P=a^2 x+b^2 ( c^2 x ) Now, d P d x =0 a^2- b^2 c^2 x^2 =0 aligned & y= c^2 b c a = a c^2 b c = a c b & a^2= b^2 c^2 x^2 x= b c a & P_ =a^2 ( b c a )+b^2 ( a c b ) & = abc + abc =2 abc . aligned