An algebra problem by A Former Brilliant Member

Algebra Level pending

If ( m + 2 ) ( m 2 − 4 ) = ( m + 2 ) q ( m − 2 ) (m+2) (m^2-4)=(m+2)^q (m-2) for all values of m m , what is the value of q q ?


The answer is 2.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Factor the left side.

( m + 2 ) ( m + 2 ) ( m − 2 ) = ( m + 2 ) q ( m − 2 ) (m+2) (m+2) (m-2) = (m+2)^q (m-2)

( m + 2 ) 2 = ( m + 2 ) q (m+2)^2 = (m+2)^q

2 = q 2 = q

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