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If `x,y` and`z` are three real numbers such that `x+y+z=4` and `x^2+y^2+z^2=6`,then show that each of x,y and z lie in the closed interval `[2/3,2]`

A

(-1,1)

B

[0,2]

C

[2,3]

D

`[2/3,2]`

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The correct Answer is:
D
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