The teacher is wrong!

Algebra Level 3

John was given a math question.

Find a solution to a + b c d = b + a c d = c + a b d = d + a b c = 2 a+bcd=b+acd=c+abd=d+abc=2

He solves it as follows:

Step 1: Rearrange into: b c d − a c d = b − a bcd-acd=b-a

Step 2: Factorise into: c d ( b − a ) = b − a cd(b-a)=b-a

Step 3: Divide: c d = 1 cd=1

Step 4: Apply to each and every equation: a b = a c = a d = b c = b d = c d = 1 ab=ac=ad=bc=bd=cd=1

Step 5: Compare to get a = b = c = d = 1 a=b=c=d=1 as one of the solution.

However, his teacher marked him wrong!

What went wrong?

Step 4 Step 3 Step 2 The teacher is wrong!

Tan Wee Kean by Tan Wee Kean , 20, Singapore

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1 solution

Highry Tan
Sep 11, 2014

You cannot just divide b-a in the equation, since b - a can be equal to 0, or a can be equal to b.

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