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

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

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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 are four distinct positive numbers in G.P.then show that a+d>b+c.

Knowledge Check

  • If a, b, c, d are distinct positive numbers in A.P., then:

    A
    a+d = b+c
    B
    a + c = b + d
    C
    a + d = 2 (b + c)
    D
    a + d = 3 (b + c)

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

    A
    `1/a+1/d gt 1/b+ 1/c`
    B
    `1/a+1/d lt 1/b+1/c`
    C
    `1/b+1/c gt 4/(a+d)`
    D
    `1/a+1/d=1/b+1/c`

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