IIT JEE , AIEEE Forum - Mathematics , Algebra

sandy1990

one could be x=y=z

dinesh_ddt

x=y=z=0 is one soln

hsbhatt

I am looking for all solutions. x=y=z=0 is one. Are there any other. Your working should be able to exhaust all possibilities.

sandy1990

x=y=z=1/2

sandy1990

did u get it
i think it is the last possible solution

hsbhatt

did who get it?

akhil_o

i am not sure if we can do this, but by symmetry
x=y=z=a

so

4a²/(4a²+1)=a

so if a not equal to 0

4a=4a²+1

(2a-1)²=0
2a=1
or a=1/2

substituting a=0
works

so values of
a=x=y=z={0,1/2}

sandy1990

solved kya

sandeepramesh

WLOG assume 1>x>=y>=z>=0

Clearly from eqn1 and eqn3 making eqn3>=eqn1 we get z>=x which is a contradiction So x=y=z

so solving the quadratic eqns, x=y=z ={0,1/2}

sandy1990

thats wht i said

sandeepramesh

sorry, but where did you say that? im sorry i didnt see it :)

sandy1990

i think it was not posted on web
i told after the ans i gave

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