QUADRATIC EQUATIONS
∴ Two numbers are 14 and 13
1
Q.
Find two numbers whose sum is 27 and product is 182.
Sol.
Let one of the number be x
∴
Sum of two numbers is 27
∴
Other number is (27 ‒ x)
According to the given condition,
∴
x
∴
27x
∴
∴
∴
=
182
(27 ‒ x)
x2
‒
=
182
0
=
x2
‒
27x
+
182
0
=
x2
‒
27x
+
182
x2
‒
14x
‒
13x
+
0
=
182
∴
x
∴
(x ‒14)
‒
13
=
0
(x ‒13)
0
=
∴
x ‒14 = 0
or
x ‒13 = 0
∴
x = 14
or
x = 13
If x =14,
then
14
27
‒
x
=
27
‒
13
=
If x =13,
then
13
27
‒
x
=
27
‒
14
=
What we need to find ?
x + Second Number = 27
Second Number = 27 - x
14 + 13
=
27
Calculation
182
91
13
2
7
13
1
182 × 1 = 182
‘+’ sign means adding
Let us do the prime factorization of 182
Find two factors of 182 in such a way that by adding factors we get middle number.
Since last sign is ‘+’ Give middle sign to both factors.
First Number + Second Number = 27
14
13
182
–
–
(x ‒14)
(x ‒14)
EX 4.2 3