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If x , y , z are all different real numb...

If `x , y , z` are all different real numbers, then `1/((x-y)^2)+1/((y-z)^2)+1/((z-x)^2)=(1/(x-y)+1/(y-z)+1/(z-x))^2`

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The correct Answer is:
(i) True; (ii) False
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Knowledge Check

  • The lines x/2=y/1=z/3 and (x-2)/(2)=(y+1)/(1)=(3-z)/(-3) are ….

    A
    Parallel
    B
    perpendicular
    C
    coincident
    D
    Intersecting in acute angle

  • If x,y,z are all different from zero and |{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=0 then value of x^(-1)+y^(-1)+z^(-1) is ".........."

    A
    xyz
    B
    `x^(-1).y^(-1).z^(-1)`
    C
    `-(xyz)`
    D
    -1

  • The lines (x-1)/(3) = (y-1)/(-1) = (z+1)/0 and (x-4)/(2) = (y+0)/(0) = (z+1)/(3) are ......

    A
    do not intersect
    B
    Intersect
    C
    Intersect at a point (4, 0,-1)
    D
    Intersect at a point (4,0,-1)

    • Similar Questions

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    Prove that |{:(x^2,y^2,z^2),((x+1)^2,(y+1)^2,(z+1)^2),((x-1)^2,(y-1)^2,(z-1)^2):}|=-4(x-y)(y-z)(z-x)

    The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)/(1) are coplanar, if

    If a ,\ b ,\ c >0\ a n d\ x ,\ y ,\ z in R , then the determinant |\ \ (a^x+a^x)^2(a^x-a^(-x))^2 1(b^y+b^(-y))^2(b^y-b^(-y))^2 1(c^z+c^(-z))^2(c^z-c^(-z))^2 1| is equal to- a. a^x b^y c^x b. a^(-x)b^(-y)c^(-z)\ c. a^(2x)b^(2y)c^(2x) d. zero

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