SOLUTION: x+1 2-x 5 +5 =126

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Question 1067008: x+1 2-x
5 +5 =126
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
5%5E%28x%2B1%29+%2B+5%5E%282-x%29 = 126 ---->

x = 2.

Solved.


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Let me explain you how it SHOULD be written and posted, for your future writing:

5^(x+1) + 5^(2-x) = 126.


It was a miracle that I was able to decipher your post . . .
It may not happen next time !!



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
5^(x+1) + 5^(2-x) = 126
----
Check for an integer solution first.
5 to the power of a positive integer is a multiply of 5.
--> For the sum to be 126, one of the terms has to be 1.
5^0 = 1
Either x+1 = 0
--> x = -1
That doesn't work.
----
Or 2-x = x
--> x = 2
That works.
5^3 + 5^0 = 126
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If it had been 5^(x+1) + 5^(2-x) = 127, there would be no algebraic solution, only numerical methods.