Two natural numbers differ by 3. Find the numbers, if the sum of their reciprocals is 7/10
Answers
Answer:
the two natural numbers are 2 and 5.
Step-by-step explanation:
Let's consider the two natural numbers to be x and x+3.
(As they differ by 3)
Then, from the question we have
x
1
+
x+3
1
=
10
7
x(x+3)
x+3+x
=
10
7
x
2
+3x
2x+3
=
10
7
20x+30=7x
2
+21x
7x
2
+x−30=0
7x
2
−14x+15x−30=0
7x(x−2)+15(x−2)=0
(x−2)(7x+15)=0
x=2,
7
−15
20x+30=7x
2
+21x
7x
2
+x−30=0
7x
2
−14x+15x−30=0
7x(x−2)+15(x−2)=0
(7x+15)(x−2)=0
S0, 7x+15=0 or x−2=0
x=−15/7 or x=2
As, x is a natural number. Only x=2 is a valid solution.
Therefore, the two natural numbers are 2 and 5.
Step-by-step explanation:
Answer
Let's consider the two natural numbers to be x and x+3.
(As they differ by 3)
Then, from the question we have
x
1
+
x+3
1
=
10
7
x(x+3)
x+3+x
=
10
7
x
2
+3x
2x+3
=
10
7
20x+30=7x
2
+21x
7x
2
+x−30=0
7x
2
−14x+15x−30=0
7x(x−2)+15(x−2)=0
(x−2)(7x+15)=0
x=2,
7
−15
20x+30=7x
2
+21x
7x
2
+x−30=0
7x
2
−14x+15x−30=0
7x(x−2)+15(x−2)=0
(7x+15)(x−2)=0
S0, 7x+15=0 or x−2=0
x=−15/7 or x=2
As, x is a natural number. Only x=2 is a valid solution.
Therefore, the two natural numbers are 2 and 5.