SSC CPO SI and ASI 2011 Paper

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Question : 138 of 200

Marks: +1, -0

If

x^{2}=y+z, y^{2}=z+x, z^{2}=x+y,

then the value of

{1}/{x+1}+ {1}/{y+1}+ {1}/{z+1}

is

-1
1
2
4

Solution:

(2)Here,

x^{2}=y+z

x^{2}+x=x+y+z

x(x+1)=x+y+z

and hence

{1}/{x+1}= {x}/{x+y+z}

Similarly,

{1}/{y+1}= {y}/{x+y+z}

and

{1}/{z+1}= {z}/{x+y+z}

Now,

{1}/{x+1}+ {1}/{y+1}+ {1}/{z+1}

= {x}/{x+y+z}+ {y}/{x+y+z}+ {z}/{x+y+z}

{1}/{x+1}+ {1}/{y+1}+ {1}/{z+1}

= {x+y+z}/{x+y+z}=1

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