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The sum of two numbers is 7 and their product is 12. What is the sum of their reciprocals?
- a)7/12
- b)8/15
- c)7/13
- d)12/7
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The sum of two numbers is 7 and their product is 12. What is the sum o...
GIVEN:
Sum of two numbers = 7
Product of two numbers = 12
Sum of two numbers = 7
Product of two numbers = 12
CALCULATION:
Let, two numbers are x and y
Sum of these two numbers is 7
x + y = 7 ----(1)
Product of these two numbers is 12
xy = 12 ----(2)
Divide equation (1) by xy
x/xy + y/xy = 7/xy
1/y + 1/x = 7/12
∴ Sum of their reciprocals is 7/12
Let, two numbers are x and y
Sum of these two numbers is 7
x + y = 7 ----(1)
Product of these two numbers is 12
xy = 12 ----(2)
Divide equation (1) by xy
x/xy + y/xy = 7/xy
1/y + 1/x = 7/12
∴ Sum of their reciprocals is 7/12
Most Upvoted Answer
The sum of two numbers is 7 and their product is 12. What is the sum o...
Given:
The sum of two numbers is 7.
Their product is 12.
To find:
The sum of their reciprocals.
Solution:
Let's assume the two numbers to be x and y.
Step 1:
We are given that the sum of two numbers is 7.
So, we can write the equation:
x + y = 7
Step 2:
We are also given that the product of the two numbers is 12.
So, we can write the equation:
xy = 12
Step 3:
Now, we need to find the sum of their reciprocals.
The reciprocal of a number x is 1/x.
So, we need to find:
1/x + 1/y
Step 4:
To simplify the expression, let's first find the value of x and y.
From Step 1, we have:
x + y = 7
y = 7 - x
Now substitute this value of y in the equation from Step 2:
x(7 - x) = 12
7x - x^2 = 12
x^2 - 7x + 12 = 0
Factoring the quadratic equation, we get:
(x - 3)(x - 4) = 0
So, x can be either 3 or 4.
Step 5:
Let's find the value of y for each value of x.
When x = 3:
y = 7 - x
y = 7 - 3
y = 4
When x = 4:
y = 7 - x
y = 7 - 4
y = 3
Step 6:
Now, let's find the sum of their reciprocals.
When x = 3, y = 4:
1/x + 1/y = 1/3 + 1/4 = (4 + 3)/12 = 7/12
When x = 4, y = 3:
1/x + 1/y = 1/4 + 1/3 = (3 + 4)/12 = 7/12
Answer:
The sum of the reciprocals of the two numbers is 7/12. Therefore, option A is the correct answer.
The sum of two numbers is 7.
Their product is 12.
To find:
The sum of their reciprocals.
Solution:
Let's assume the two numbers to be x and y.
Step 1:
We are given that the sum of two numbers is 7.
So, we can write the equation:
x + y = 7
Step 2:
We are also given that the product of the two numbers is 12.
So, we can write the equation:
xy = 12
Step 3:
Now, we need to find the sum of their reciprocals.
The reciprocal of a number x is 1/x.
So, we need to find:
1/x + 1/y
Step 4:
To simplify the expression, let's first find the value of x and y.
From Step 1, we have:
x + y = 7
y = 7 - x
Now substitute this value of y in the equation from Step 2:
x(7 - x) = 12
7x - x^2 = 12
x^2 - 7x + 12 = 0
Factoring the quadratic equation, we get:
(x - 3)(x - 4) = 0
So, x can be either 3 or 4.
Step 5:
Let's find the value of y for each value of x.
When x = 3:
y = 7 - x
y = 7 - 3
y = 4
When x = 4:
y = 7 - x
y = 7 - 4
y = 3
Step 6:
Now, let's find the sum of their reciprocals.
When x = 3, y = 4:
1/x + 1/y = 1/3 + 1/4 = (4 + 3)/12 = 7/12
When x = 4, y = 3:
1/x + 1/y = 1/4 + 1/3 = (3 + 4)/12 = 7/12
Answer:
The sum of the reciprocals of the two numbers is 7/12. Therefore, option A is the correct answer.
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