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Which of the following is the difference between the squares of two consecutive natural numbers is:
- a)sum of the two numbers
- b)difference of the numbers
- c)twice the sum of the two numbers
- d)twice the difference between the two numbers.
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Which of the following is the difference between the squares of two co...
Explanation:
Let's consider two consecutive natural numbers as x and x+1. Then the difference between their squares will be:
(x+1)^2 - x^2
= x^2 + 2x + 1 - x^2 [Expanding the square]
= 2x + 1
This expression is equal to the sum of the two numbers (x + x+1).
Therefore, the correct answer is option 'A' which states that the difference between the squares of two consecutive natural numbers is the sum of the two numbers.
Example:
Let's take two consecutive natural numbers, say 5 and 6.
The square of 5 is 25 and the square of 6 is 36.
The difference between their squares is 36 - 25 = 11.
The sum of 5 and 6 is 11.
Hence, the difference between the squares of two consecutive natural numbers (11) is equal to the sum of the two numbers (5 + 6 = 11).
Therefore, the answer is verified.
Let's consider two consecutive natural numbers as x and x+1. Then the difference between their squares will be:
(x+1)^2 - x^2
= x^2 + 2x + 1 - x^2 [Expanding the square]
= 2x + 1
This expression is equal to the sum of the two numbers (x + x+1).
Therefore, the correct answer is option 'A' which states that the difference between the squares of two consecutive natural numbers is the sum of the two numbers.
Example:
Let's take two consecutive natural numbers, say 5 and 6.
The square of 5 is 25 and the square of 6 is 36.
The difference between their squares is 36 - 25 = 11.
The sum of 5 and 6 is 11.
Hence, the difference between the squares of two consecutive natural numbers (11) is equal to the sum of the two numbers (5 + 6 = 11).
Therefore, the answer is verified.
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Which of the following is the difference between the squares of two co...
Option a
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