You can put this solution on YOUR website! This one is a bit tricky. We have to think out how we can take a number and reise it to a power and get a result of 1. There are three possibilities I can think of:
1 to any power is 1
Any number (excpet zero) to the zero power is 1
-1 to any even power is 1
So we will look for solutions from all three possibilities.
1 to any power is 1:
Solve
Subtract 1 from each side:
Factor:
Use the Zero Product Property: or
Solve: or
Any number but zero to the zero power is 1
For this we will find the x's that make and then check to make sure they do not make zero, too. Solving ...
Factor:
Use the Zero Product Property: or
Solve: or
Now we check to see if either of these make zero:
for x = 4: This is not 0 so x = 4 is OK.
for x = 5: This is not 0 so x = 5 is OK.
-1 to an even power is 1
Solve and then see if is even for those x's.
Solve :
Add 1 to each side:
Factor:
Use the Zero Product Property: or
Solve:
x = 3 or x = 2
Now we will see if either of these make the exponent, , even:
for x = 3: This is even so x = 3 is a solution.
Now we will see if either of these make the exponent, , even:
for x = 2: This is also even so x = 2 is also a solution.
So the solutions are: x = 4, x = 1, x = 5, x = 3 and x = 2.
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