Module-1 Algebra Quadratic Equations Worksheet With Answers Page 10
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14MODULE -
1
Quadratic Equations
Algebra
or
10x – x + y – 10y = – 9
or
9x – 9y = –9
or
x – y = – 1
Notes
or
x = y – 1
...(1)
Also, product of digits is 12
Hence,
xy = 12
...(2)
Substituting value of x from (1) into (2), we get
(y – 1)y = 12
2
or
y
– y – 12 = 0
or
(y – 4) (y + 3) = 0
Hence,
y = 4 or y = – 3
Since, digit can not be negative, y = 4
Hence x = y – 1 = 4 – 1 = 3
Therefore, the number is 34.
4
Example 6.12:
The sum of two natural numbers is 12. If sum of their reciprocals is
,
9
find the numbers.
Solution:
Let one number be x
Therefore, other number = 12 – x
4
Since, sum of their reciprocals is
, we get
9
1
1
4
+
=
≠
−
≠
,
x
0,
12
x
0
−
x
12
x
9
−
+
12
x
x
4
=
or
(
)
−
x
12
x
9
12
4
=
or
−
2
12x
x
9
×
12
9
=
−
2
12x
x
or
4
2
or
27 = 12x – x
Mathematics Secondary Course
179
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