390 algebra De mystif ieD
- Let x = first number and x + 1 = second number.
xx
xx
xx
xx
()
()()
+=
+=
+− =
+−=
1 380
380
380 0
20 19 0
2
2
x
x
x
+=
=−
+=−
20 0
20
119
x
x
x
−=
=
+=
19 0
19
120
There are two solutions: 19 and 20, and −19 and −20.
- Let x = first number and x + 1 = second number.
xx
xx
xx
xx
()
()()
+=
+=
+− =
−+=
1 650
650
650 0
25 26 0
2
2
x
x
x
−=
=
+=
25 0
25
126
x
x
x
+=
=−
+=−
26 0
26
125
There are two solutions: 25 and 26, and −25 and −26.
- Let x = first number and x + 2 = second number.
xx
xx
xx
xx
()
()()
+=
+=
+−=
−+=
2 288
2 288
2 288 0
16 18 0
2
2
x
x
x
−=
=
+=
16 0
16
218
x
x
x
+=
=−
+=−
18 0
18
216
There are two solutions: 16 and 18, and −16 and −18.