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If tan -1 x+tan -1 y+tan -1 z=/2 and (x-y)²+(y-z)²+(z-x)²=0,then x 2 +y 2 +z 2 equals a.0 b.4 c.1 d.none of these

If tan-1x+tan-1y+tan-1z=/2 and (x-y)²+(y-z)²+(z-x)²=0,then x2+y2+z2 equals


a.0


b.4


c.1


d.none of these

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Meanka,

As each of the sqaure term in the sum≥0, the sum can be zero, only when x=y=z.

So 3tan-1x= pie/2 (i assume you missed pie in the question). So x = tan(pie/6) = 1/root(3).

So the required sum = 1. Option (C).

 

Hope that helps.

 

Best Regards,

Ashwin (IIT Madras).

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