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What are the two natural numbers whose product is 2400 and the sum of whose squares is 5200?
- a)80,30
- b)75, 32
- c)60, 40
- d)120, 20
- e)None of the above/More than one of the above
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
What are the two natural numbers whose product is 2400 and the sum of ...
Explanation:
Given:
Product of two numbers = 2400
Sum of squares of the two numbers = 5200
Let the two numbers be x and y:
xy = 2400
x^2 + y^2 = 5200
Finding the two numbers:
Step 1: Finding the two numbers using the product:
We need to find two numbers whose product is 2400.
Factors of 2400 are:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 200, 240, 300, 400, 600, 1200, 2400
From the factors, the pair that satisfies the given condition is 60 and 40 since 60 * 40 = 2400.
Step 2: Finding the two numbers using the sum of squares:
We need to find two numbers whose sum of squares is 5200.
Substitute x = 60 and y = 40 into the equation:
60^2 + 40^2 = 3600 + 1600 = 5200
Therefore, the two natural numbers are 60 and 40.
Conclusion:
The two natural numbers whose product is 2400 and the sum of whose squares is 5200 are 60 and 40. Hence, option 'C' is the correct answer.
Given:
Product of two numbers = 2400
Sum of squares of the two numbers = 5200
Let the two numbers be x and y:
xy = 2400
x^2 + y^2 = 5200
Finding the two numbers:
Step 1: Finding the two numbers using the product:
We need to find two numbers whose product is 2400.
Factors of 2400 are:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 200, 240, 300, 400, 600, 1200, 2400
From the factors, the pair that satisfies the given condition is 60 and 40 since 60 * 40 = 2400.
Step 2: Finding the two numbers using the sum of squares:
We need to find two numbers whose sum of squares is 5200.
Substitute x = 60 and y = 40 into the equation:
60^2 + 40^2 = 3600 + 1600 = 5200
Therefore, the two natural numbers are 60 and 40.
Conclusion:
The two natural numbers whose product is 2400 and the sum of whose squares is 5200 are 60 and 40. Hence, option 'C' is the correct answer.
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Community Answer
What are the two natural numbers whose product is 2400 and the sum of ...
The correct answer is option (3), 60 and 40.
Let the numbers are A and B;
Given
AB = 2400 .....(1)
and A2 + B2 = 5200
We know that
(A + B)2 = A2 + B2 + 2AB = 5200 + 4800 = 10000
Or, A + B = 100 .....(2)
By solving equation (1) and (2)
We get a and b = 60 and 40.
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What are the two natural numbers whose product is 2400 and the sum of whose squares is 5200?a)80,30b)75, 32c)60, 40d)120, 20e)None of the above/More than one of the aboveCorrect answer is option 'C'. Can you explain this answer?
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