If a, b, c are three unequal positive number in HP then `a)a^100+c^100 gt 2b^100 b) a^3+c^3>2b^3 c) a^5+c^5>2b^5 d)a^2+c^2>2b^2`

If three unequal positive numbers a, b, c are in G.P. then show that, a +c gt 2b .

If a,b,c are three distinct positive real numbers which are in H.P., then (3a + 2b)/(2a - b) + (3c + 2b)/(2c - b) is

If a ,\ b ,\ c are positive real numbers, then root(5)(3125\ a^(10)b^5c^(10)) is equal to (a)\ 5a^2b c^2 (b) 25 a b^2c (c) 5a^3b c^3 (d) 125\ a^2b c^2

If a,b,c are positive unequal real numbers then prove that b^2c^2+c^2a^2+a^2b^2gtabc(a+b+c) .

If a,b,c are positive unequal real numbers then prove that a^2+b^2+c^2gtab+bc+ca . Hence prove that a^3+b^3+c^3gt3abc

If three positive real numbers a,b,c, (cgta) are in H.P., then log(a+c)+log(a-2b+c) is equal to

If three positive real numbers a,b,c, (cgta) are in H.P., then log(a+c)+log(a-2b+c) is equal to

Suppose a, b, c are positive resl numbers different from 1. If log_(a) 100, 2 log_(b) 10, 2 log_(c) 5 + log_(c) 4 are in H.P., then a, b , c are in