If a + b b + c = c + d d + a then..(A) a = c(B) either a = c or a + b + c + d = 0(C) a + b + c + d = 0(D) a = c and b = dI solved a + b b + c = c + d d + a and got a ( a + b + d ) = c ( c + b + d ) and so I thought that (A) is the correct option. But the correct answer is (B).I'm how a + b b + c = c + d d + a if a + b + c + d = 0. Please help.

Question

If             a      +      b              b      +      c        =            c      +      d              d      +      a       then..(A)   a  =  c(B) either   a  =  c or   a  +  b  +  c  +  d  =  0(C)   a  +  b  +  c  +  d  =  0(D)   a  =  c and   b  =  dI solved             a      +      b              b      +      c        =            c      +      d              d      +      a       and got   a  (  a  +  b  +  d  )  =  c  (  c  +  b  +  d  ) and so I thought that (A) is the correct option. But the correct answer is (B).I&#039;m how             a      +      b              b      +      c        =            c      +      d              d      +      a       if   a  +  b  +  c  +  d  =  0. Please help.

seraphinod · Accepted Answer

Hint: we get by cross multiplication      a    2    +  a  b  +  a  d  +  b  d  =  b  c  +  b  d  +      c    2    +  d  cfrom here we get  a  b  −  b  c  +  a  d  −  c  d  +      a    2    −      c    2    =  0or  (  a  −  c  )  (  a  +  b  +  c  +  d  )  =  0

xonycutieoxl1 · Accepted Answer

If   a  +  b  +  c  +  d  =  0, then   (  a  +  b  )  =  −  (  c  +  d  ) and   (  b  +  c  )  =  −  (  a  +  d  ), therefore             a      +      b              b      +      c        =            −      (      c      +      d      )              −      (      a      +      d      )        =            c      +      d              a      +      d      provided that we don&#039;t divide by zero anywhere.

If a + b </mrow> b + c </mrow>

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