Algebra Demystified 2nd Ed

390 algebra De mystif ieD

2. 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.

3. 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.

4. 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.