Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23
Solution:
Let x be the smaller of the two consecutive even positive integers, then the other integer is (x + 2)
Since both the integers are larger than 5,
x > 5 ....(1)
Also, the sum of the two integers is less than 23
x + (x + 2) < 23
⇒ 2x + 2 < 23
⇒ 2x < 21
⇒ x < 21/2
⇒ x < 10.5. ....(2)
From (1) and (2), we obtain
5 < x <10.5.
Since x is an even positive integer, then values of x are 6, 8 and 10
When When When
x = 6, the pair is (6, 8)
x = 8, the pair is (8, 10)
x = 10, the pair is (10, 12)
Thus, the required possible pairs are (6, 8), (8, 10) and (10, 12)
NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.1 Question 24
Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23
Summary:
A linear inequation x + (x + 2) < 23 can be formed. We have found that the required possible pairs are (6, 8), (8, 10) and (10, 12)
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