If a,b , c are distinct +ve real numbers and `a^(2)+b^(2)+c^(2)=1" then "ab+bc+ca` is

If a ,b , a n dc are distinct positive real numbers such that a+b+c=1, then prove tha ((1+a)(1+b)(1+c))/((1-a)(1-b)(1-c))> 8.

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 a, b, d and p are distinct non - zero real numbers such that (a^2+b^2 + c^2) p^2 - 2(ab+bc+cd)p+(b^2 + c^2 +d^2) le 0 then n. Prove that a, b, c, d are in G. P and ad = bc

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

If a ,b ,c ,da n dp are distinct real numbers such that (a^2+b^2+c^2)p^2-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0, then prove that a ,b ,c , d are in G.P.

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 and c are distinct positive real numbers in A.P, then the roots of the equation ax^(2)+2bx+c=0 are

If a,b,c are positive real numbers and 2a+b+3c=1 , then the maximum value of a^(4)b^(2)c^(2) is equal to

If a,b,c,d are positive real number with a + b + c + d=2 ,then M =(a+b)(c+d) satisfies the inequality