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Evaluate each of the following express...

Evaluate each of the following expressions for `x=-2,\ y=-1,\ z=3:` (i) `x/y+y/z+z/x` (ii) `x^2+y^2+z^2-x y-y z-z x`

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Evaluate each of the following algebraic expressions for x=1,\ y=-1, z=2,\ a=-2,\ b=1,\ c=-2: (i) a x+b y+c z (ii) a x^2+b y^2-c z^2 (iii) a x y+b y z+c x y

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Knowledge Check

  • The value of the expression ((x ^(2) - y ^(2)) ^(3) + ( y ^(2) - z ^(2)) ^(3) + (z ^(2) - x ^(2)) ^(3))/((x - y) ^(3) + ( y - z) ^(3) + (z - x ) ^(3)) is

    A
    `(x ^(2) - y ^(2)) (y ^(2) - z ^(2)) ( z ^(2) - x ^(2))`
    B
    `3 (x - x ) ( y -z) (z -x)`
    C
    `(x + y) (y + z) (z + x)`
    D
    `(3 (x + y) (y + z) (z + x)`

  • The values of x, y, z for the equations x-y+z=1, 2x-y=1, 3x+3y-4z=2 are

    A
    `x=2, y=3, z=5`
    B
    `x=1, y=1, z=1`
    C
    `x=1, y=-1, z=-1`
    D
    `x=3, y=1, z=2`

  • Evaluate the expression ((x-y)^(3) + (y-z)^(3) + (z-x)^(3) )/( (x-y) (y-z) + (z-x) ) in the simplest form.

    A
    1
    B
    2
    C
    3
    D
    `-1`

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