If a,b,c are three distinct positive real numbers in G.P., than prove that `c^2+2ab gt 3ac`.

If a , b ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3ac

If a,b,c are distinct positive real numbers, then

If a, b, c, d are distinct positive numbers in A.P., then:

If a ,b ,c ,d are four distinct positive numbers in G.P. then show that a+d > b+c dot

If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , then prove that either x 3

If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , then prove that either x >3.

If a, b, c are distinct positive real numbers in G.P and log_ca, log_bc, log_ab are in A.P, then find the common difference of this A.P

If the parabolas y^2=4a x and y^2=4c(x-b) have a common normal other than the x-axis (a , b , c being distinct positive real numbers), then prove that b/(a-c)> 2.

If the parabolas y^2=4a x and y^2=4c(x-b) have a common normal other than the x-axis (a , b , c being distinct positive real numbers), then prove that b/(a-c)> 2.

If a ,b ,c are three distinct positive real numbers, the number of real and distinct roots of a x^2+2b|x|-c=0 is 0 b. 4 c. 2 d. none of these