Question

if x+y+z=1 xy+yz+zx=2,xyz=-3 then prove 1/x+yz +1/y+zx +1/z+xy=2

Answer 1

Thank you for asking this question. Here is your answer:

xyz=1

1/y=xz

similarly,

1/z=xy,1/x=yz

1/(1 +x +xz) + 1/(1+y+xy)+1/(1+z+yz)

=y/y*(1/1+x+xz) + 1/(1+y+xy) + xy/xy*(1/1+z+yz)

=(y/y+yx+xyz ) +1/(1+y+xy) + (xy/xy+xyz+xy*yz)

=y/y+xy+1 + 1/(1+y+xy) +{xy/xy+1+(xyz*y)} ……………..(xyz=1)

=y/y+xy+1 + 1/(1+y+xy) + xy/xy+1+(1*y)

=y/y+xy+1 + 1/(1+y+xy) +xy/xy+1+y

=y+1+xy/y+xy+1

=1

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