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 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 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 a,b,c,d be four consecutive coefficients in the binomial expansion of (1+x)^(n) , then value of the expression (((b)/(b+c))^(2)-(ac)/((a+b)(c+d))) (where x gt 0 and n in N ) is

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 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 ,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 and d are four coplanr points, then prove that [a b c]=[b c d]+[a b d]+[c a d] .

If a,b and c are any three vectors in space, then show that (c+b)xx(c+a)*(c+b+a)= [a b c]

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) .