Question 152: two consecutive integers are added the square of their sum is 361, what are the integers? Found 2 solutions by terrtwo, abhishek425:Answer by terrtwo(10) (Show Source):
You can put this solution on YOUR website! First before we make an equation, we need to define the variables:
if the first number is X, then since they are consecutive the other variable should be (X +1).
Adding those two integers --> = X + (X + 1) --> 2X + 1
The square of their sum is listed thusly --> (2X + 1)^2 = 361
When we take the square of both side (no need to complete the square here) -->
2X + 1 = 19.
We then subtract 1 from both sides --> 2X + 1 - 1 = 19 -1 --> 2X -18.
We divide both sides by 2 --> 2X/2 = 18/2 --> X = 9.
Since we defined X to be the first number, X + 1 is the next number
--> X +1 = 9 + 1 = 10.
The comsecutive numbers are 9 and 10
You can put this solution on YOUR website! if the first number is X, then since they are
consecutive the other variable should be (X +1).
Adding those two integers --> = X + (X + 1) -->
2X + 1 The square of their sum is listed thusly --> (2X +
1)^2 = 361
When we take the square of both side (no need
to complete the square here) -->
2X + 1 = 19.
We then subtract 1 from both sides --> 2X + 1 - 1 = 19 -1 --> 2X -18.
We divide both sides by 2 --> 2X/2 = 18/2 --> X
= 9.
Since we defined X to be the first number, X + 1
is the next number
--> X +1 = 9 + 1 = 10. The comsecutive numbers are 9 and 10
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