Let a ,b ,c ,d be four distinct real nu...

Let `a ,b ,c ,d` be four distinct real numbers in A.P. Then half of the smallest positive valueof `k` satisfying `2(a-b)+k(b-c)^2+(c-a)^3=2(a-d)+(b-d)^2+(c-d)^3` is __________.

Similar Questions

Explore conceptually related problems

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.

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

Let a,b,c,d be real numbers such that |a-b|=2, |b-c|=3, |c-d|=4 Then the sum of all possible values of |a-d|=

If a,b,c and d are four unequal positive numbers which are in A.P then

a,b,c,d are four different real numbers which are in APIf 2(a-b)+x(b-c)^(2)+(c-a)^(3)=2(a-d)+(b-d)^(2)+(c-d)^(3), then

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 distinct numbers in A.P then show that (1)/(a)+(1)/(d)>(1)/(b)+(1)/(c)>(4)/(a+d)

If a,b,c,d are distinct integers in A.Puch that d=a^(2)+b^(2)+c^(2), then a+b+c+d is

Let a,b,c be three distinct positive real numbers then number of real roots of ax^2+2b|x|+c=0 is (A) 0 (B) 1 (C) 2 (D) 4