SOLUTION: 5^x+5^y=150, x-y=1, Solve Simultaneously

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Question 1148189: 5^x+5^y=150, x-y=1, Solve Simultaneously
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


By inspection....

We need to add two powers of 5 to get a sum of 150. Since that sum is a whole number, the powers have to be integers.

5^1 = 5
5^2 = 25
5^3 = 125

25+125 = 150; so x and y are 2 and 3.

Then, since we are told that x-y=1, x is 3 and y is 2.

If you need an algebraic solution....

x-y=1 --> x = y+1

Then

5%5Ex%2B5%5Ey=150
5%5E%28y%2B1%29%2B5%5Ey+=+150
5%2A%285%5Ey%29%2B5%5Ey+=+150
6%2A5%5Ey+=+150
5%5Ey+=+25
y+=+2
x+=+y%2B1+=+3