If a,b,c,d are four distinct positive numbers in A.P., then show that bc>ad.

If a,b,c,d be four distinct positive quantities in GP,then show that (a) a+dgtb+c

If a,b,c,d be four distinct positive quantities in HP, then (a) a+dgtb+c (b) adgt bc

If A and G are the A.M. and G.M. respectively between any two distinct positive numbers a and b then show that A > G.

If G is the geometric mean between two distinct positive numbers a and b, then show that 1/(G-a)+1/(G-b)=1/G .

If a,b,c,d are distinct integers in an A.P. such that d=a^(2)+b^(2)+c^(2) , then find the value of a+b+c+d.

If a ,b ,c ,d are four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b. real and equal c. integers d. real and distinct

If a,b,c are in A.P. then :

If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c-a).z(a-b)=1 .

If a,b,c and d are four positive real numbers such that abcd=1 , what is the minimum value of (1+a)(1+b)(1+c)(1+d) .

Let a,b,c,d be positive real numbers with altbltcltd . Given that a,b,c,d are the first four terms of an AP and a,b,d are in GP. The value of (ad)/(bc) is (p)/(q) , where p and q are prime numbers, then the value of q is _____