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If x+y +z=0, then (x+y) (y+z) (z+x) is ...

If `x+y +z=0`, then `(x+y) (y+z) (z+x)` is equal to which of the following:

A

`-xyz`

B

`x^(2)+y^(2)+z^(3)`

C

`x^(3)+y^(3) +z^(3)+3xyz`

D

xyz

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • Following functions are defined for three distinct positive numbers, such that x lt y lt z. f(x,y,z) = min (max (x+y, y+z), max (z+x, x+y)) g(x,y,z) = max (min (x+y, y+z), min (z+x, x+y)) h(x, y, z) = max (max (x+y, y+z), max (z+x, x+y)) j(x,y,z) = min(min(x+y, y+z), min (z+x, x+y)) k(x, y, z) = int. ((x+y, y+z)//3 such that k(x,y,z) le (x+y+z)//3 l(x, y, z) = min (x, y, z), m (x, y, z) = max (x, y, z) Which of the following expression is necessarily equal to 1?

    A
    55
    B
    65
    C
    57
    D
    45

  • Following functions are defined for three distinct positive numbers, such that x lt y lt z. f(x,y,z) = min (max (x+y, y+z), max (z+x, x+y)) g(x,y,z) = max (min (x+y, y+z), min (z+x, x+y)) h(x, y, z) = max (max (x+y, y+z), max (z+x, x+y)) j(x,y,z) = min(min(x+y, y+z), min (z+x, x+y)) k(x, y, z) = int. ((x+y, y+z)//3 such that k(x,y,z) le (x+y+z)//3 l(x, y, z) = min (x, y, z), m (x, y, z) = max (x, y, z) Which of the following expression given negative value?

    A
    `7/3`
    B
    `5/3`
    C
    `5/2`
    D
    `3/2`

  • If (x+y)/(x+y+z)=(y+z)/(x+y+z)=(x+z)/(x+y+z)=p , then which of the following can be the value of p?

    A
    `1/2`
    B
    2
    C
    `2/3`
    D
    3

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