Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Find all real numbers a such that

a2=a−2.

Explain why this does not violate the exponential function property which states

ax=ay

if and only if

x=y.
 
Expert Solution
Check Mark
Step 1

a2 = a-2 implies, a2 = 1/a2 

Then, a4 = 1

So, a4 - 1 = 0

i.e. (a² - 1)(a²+1) = 0

Since, a² + 1 > 0 for all real a, we only have,

a² - 1 = 0

i.e. a = 1, - 1

So, the solution is, a = 1 & - 1

 

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