` a, b, c, d` are four different real numbers which are in AP.If `2(a - b) +x (b-c)^2 + (c-a)^3 = 2 (a-d) + (b - d)^2 + (c-d)^3`, 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 four non - zero real numbers such that (d+a-b)^(2)+(d+b-c)^(2)=0 and roots of the equation a(b-c)x^(2)+b(c-a)x+c(a-b)=0 are real equal, then

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)

If a, b, c, d, e are positive real numbers, such that a + b +c + d + e = 8 and a^2 + b^2 + c^2 + d^2 + e^2 = 16 , find the range of e.

If a, b, c and d are four positive real numbers such that sum of a, b and c is even the sum of b,c and d is odd, then a^2-d^2 is necessarily

If a,b,c,d are positive real numbers such that (a)/(3) = (a+b)/(4)= (a+b+c)/(5) = (a+b+c+d)/(6) , then (a)/(b+2c+3d) is:-

If (2a+3b) (2c -3d) = (2a-3b) (2c+3d) then

If a,b,c,d be in G.P. show that (b-c)^2+(c-a)^2+(d-b)^2=(a-d)^2.

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