QUADRATIC �EQUATIONS
| |||
| | | |
| | | |
| | | |
| | | |
| | | |
WORD PROBLEMS BASED ON CONSECUTIVE NUMBERS
2 Consecutive Numbers
3 Consecutive Numbers
4 Consecutive Numbers
2 Consecutive
ODD Numbers
2 Consecutive
EVEN Numbers
5
5
5
3
4
5
5
3
4
x
x
x
x
x
How do we express 6 in terms of 5 ?
, 6
, 6
, 7
, 6
, 7
, 8
, 5
, 6
, 5+1
, 5+1
, 5+2
, 5+1
, 5+2
, 5+3
, 3+2
, 4+2
How do we express 6 in terms of 5 ?
How do we express 7 in terms of 5 ?
How do we express 6 in terms of 5 ?
How do we express 7 in terms of 5 ?
How do we express 8 in terms of 5 ?
How do we express 5 in terms of 3 ?
How do we express 6 in terms of 4 ?
, x+1
, x+1
, x+2
, x+1
, x+2
, x+3
, x+2
, x+2
5
or x – 7 = 0
or x = 7
1
Sol.
As per the given condition,
+
( )2
=
113
x2 +
2x2
2x2 + 2x – 112 = 0
x2 + x – 56 = 0
x2
∴
∴
∴
∴
∴
Dividing throughout by 2
x2 + 2x + 1
x
(x + 8)
x + 8 = 0
∴
∴
∴
Let the two consecutive natural numbers be x and x+1.
( )2
x
x+1
x = – 8
The required numbers are natural numbers
x ≠ -8
Hence, x = 7
∴
∴
∴
and x + 1
The two required consecutive natural numbers are 7 and 8.
∴
(a+b)2 = a2 + 2ab + b2
How many numbers?
Means +
Square of what ?
What will be the two consecutive natural numbers ?
x and x + 1
Find two factors of 56 in such a way that by subtracting factors we get middle number 1
8
7
56
8 – 7 = 1
Since we are subtracting the factors give middle term sign to the bigger factor and the opposite sign to the smaller factor
+
–
+ 8x
– 7x
– 56
= 0
(x + 8)
– 7
(x + 8)
= 0
(x – 7)
= 0
= 7 + 1
= 8
= 113
+ 2x
+ 1
– 113
= 0
What we need to find ?
Q) The sum of the squares of two consecutive natural numbers is 113. Find the numbers.