Sum of two natural numbers is 8 and the difference of their reciprocals is . Find the numbers??
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Answers
Answer:-
The numbers are
• Given:-
Sum of two natural numbers is 8.
Difference of their reciprocals is 2/15
• To Find:-
The numbers
• Solution:-
Let the numbers be 'x' and 'y'.
• According to the question:-
✴
✴
• Taking eqn[i]:-
• Substituting this value of x in eqn[ii]:-
• Taking LCM:-
• Cross multiplying:-
• Splitting the middle term:-
Now,
Here, y = -12 is not possible.
Hence,
• Substituting the value of y in eqn[i]:-
Therefore, the numbers are 3 and 5.
Answer:
Given :
- Sum of two natural numbers is 8 .
- the difference of their reciprocals is 2/15 .
To Find :
- Find the numbers??
Solution :
Let the numbers be a and b
According to the Question :
a + b = 8
- b = 8 - a .......( i )
1/b - 1/a = 2/15
- a - b = (2/15) × ab .........( ii )
Adding (I) and (ii), we get :
2a = 8 + 2ab/15
30a = 120 + 2ab
Substitute the value of b ;
Therefore,
30a = 120 + 2a(8 - a)
30a = 120 + 16a - 2a²
30a - 16a + 2a² = 120
2a² + 14a - 120 = 0
a² + 7a - 60 = 0
- [ dividing by 2 throughout ]
a² + 12a - 5a = 0
(a + 12)(a - 5) = 0
a = -12 or a = 5
As "a" is a natural number, a = -12 is inadmissible then a = 5
Using (i), we get b = 8 - a
Substitute all Values :
b = 8 - 5
b = 3
The required numbers are 5 and 3
Verification:
Sum of given numbers = 5 + 3 = 8
Difference of reciprocals = 1/3 - 1/5 = 2/15