A binary operation x is defined by \(a \mathbin{x} b = a^b\). If \(a \mathbin{x} 2 = 2 - a\), find the possible values of \(a\)?
Question 1 Report
A binary operation x is defined by \(a \mathbin{x} b = a^b\). If \(a \mathbin{x} 2 = 2 - a\), find the possible values of \(a\)?
Answer Details
The equation a x 2 = 2 - a can be solved for the possible values of a. To do this, we can simplify the equation by adding a to both sides:
a x 2 + a = 2
Combining like terms:
a x 2 + a = 2
a(x + 1) = 2
Dividing both sides by x + 1:
a = 2 / (x + 1)
Since the binary operation x is defined as a x b = a, we can substitute this definition into the equation:
a = 2 / (a x 1 + 1)
a = 2 / (a + 1)
Since a x b = a, we know that a x 1 = a, so we can substitute this into the equation:
a = 2 / (a + 1)
a = 2 / (a + 1)
Solving for a, we get:
a = 2 / (a + 1) = 2 / (2) = 1
So, the possible values of a are 1.
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