Try to Solve Without Graphing
Algebra
Level
4
Given the domain [-10, 10], determine how many values of x (x values are integers) yield a square for the result of the equation:
3
4
2
1
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1 solution
First, we can get rid of a common factor: x 2 ( 2 x + 3 ) Now we know that x = 0 is one of the the solutions within the domain. Now all we need do is find the zeroes from the second half of the equation: A 2 = ( 2 x + 3 ) = 2 ( x + 1 ) + 1 Now, we can say for certain A 2 ≡ 0 ( m o d 2 ) . We may use substitution here with ( x + 1 ) : 2 m + 1 And finally set m equal to m < 2 : m = 0 , A = ± 1 , x = − 1 m = 1 , A = 3 o r − 1 , x = − 1 o r 3 We are left with the set of correct integers: { − 1 , 0 , 3 }