Line 1: x² + 3x + 2, (x + 1)(x + 2), (x + 1.5)² − 0.25
Line 2: x² + 5x + 6, (x + 2)(x + 3), (x + 2.5)² + 6.25
If two expressions are equivalent, then no matter what number
we substitute into them, they will always simplify to the
same numbers.
So let's check by substituting a value, say, x=0 in each:
Line 1: 0² + 3(0) + 2, (0 + 1)(0 + 2), (0 + 1.5)² − 0.25
Line 1: 2, 2, 2.25 − 0.25
Line 1: 2, 2, 2
Line 2: 0² + 5(0) + 6, (0 + 2)(0 + 3), (0 + 2.5)² + 6.25
Line 2: 6, 6, 6.25 + 6.25
Line 2: 6, 6, 12.50
Looks like the answer is Line 1 only. We have eliminated Line 2.
But we can't be sure about Line 1. That's because it might
have just been an accident that we got the same. So let's
substitute x=1 in each:
Line 1: 1² + 3(1) + 2, (1 + 1)(1 + 2), (1 + 1.5)² − 0.25
Line 1: 1+3+2, 2·3, (2.5)² − 0.25
Line 1: 6, 6, 6.25 - 0.25
Line 1: 6, 6, 6
Yes it's probably Line 1 only. For it's not
likely that we'd have run into two
accidents.
Try x = 2
Line 1: 2² + 3(2) + 2, (2 + 1)(2 + 2), (2 + 1.5)² − 0.25
Line 1: 4+6+2, 3·4, (3.5)² − 0.25
Line 1: 12, 12, 12,25 - 0.25
Line 1: 12, 12, 12
No doubt about it. It's Line 1 only.
Edwin
