Software Development Exam > Software Development Questions > The square of the difference between two give...
Start Learning for Free
The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.
- a)630
- b)540
- c)450
- d)360
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The square of the difference between two given natural numbers is 324,...
Given:
The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144.
Calculation:
Let the numbers are x and y
(x - y)2 = 324
So, x - y = 18, xy = 144
(x + y)
2
= (18)2 + 4× 144
⇒ 900
⇒ x + y = 30
Then, x is (30 + 18) / 2 = 24 and y = 6
So , x2 - y2 = 242 - 62
⇒ 576 - 36 = 540
∴ The correct option is 2
Free Test
FREE
| Start Free Test |
Community Answer
The square of the difference between two given natural numbers is 324,...
Given Information:
The square of the difference between two natural numbers is 324, while the product of these two numbers is 144.
Let's solve the problem step by step:
Step 1: Set up the equations
Let the two natural numbers be x and y. According to the given information,
1. (x - y)^2 = 324
2. xy = 144
Step 2: Solve the equations
1. (x - y)^2 = 324
Expanding the left side, we get:
x^2 - 2xy + y^2 = 324
x^2 + y^2 - 2xy = 324
2. xy = 144
Now, substitute the value of xy from equation 2 into equation 1:
x^2 + y^2 - 2*144 = 324
x^2 + y^2 = 612
Step 3: Find the positive difference between the squares of the numbers
We need to find the positive difference between x^2 and y^2.
Since x^2 + y^2 = 612, and xy = 144, we can find the squares of x and y.
x^2 = 612 - y^2
x^2 = 612 - 144
x^2 = 468
Similarly,
y^2 = 612 - x^2
y^2 = 612 - 468
y^2 = 144
Now, find the positive difference between x^2 and y^2:
|x^2 - y^2| = |468 - 144| = 324
Therefore, the positive difference between the squares of the two given natural numbers is 324.
Conclusion:
The correct answer is option B) 540.
The square of the difference between two natural numbers is 324, while the product of these two numbers is 144.
Let's solve the problem step by step:
Step 1: Set up the equations
Let the two natural numbers be x and y. According to the given information,
1. (x - y)^2 = 324
2. xy = 144
Step 2: Solve the equations
1. (x - y)^2 = 324
Expanding the left side, we get:
x^2 - 2xy + y^2 = 324
x^2 + y^2 - 2xy = 324
2. xy = 144
Now, substitute the value of xy from equation 2 into equation 1:
x^2 + y^2 - 2*144 = 324
x^2 + y^2 = 612
Step 3: Find the positive difference between the squares of the numbers
We need to find the positive difference between x^2 and y^2.
Since x^2 + y^2 = 612, and xy = 144, we can find the squares of x and y.
x^2 = 612 - y^2
x^2 = 612 - 144
x^2 = 468
Similarly,
y^2 = 612 - x^2
y^2 = 612 - 468
y^2 = 144
Now, find the positive difference between x^2 and y^2:
|x^2 - y^2| = |468 - 144| = 324
Therefore, the positive difference between the squares of the two given natural numbers is 324.
Conclusion:
The correct answer is option B) 540.
Attention Software Development Students!
To make sure you are not studying endlessly, EduRev has designed Software Development study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Software Development.
|
Explore Courses for Software Development exam
|
|
Similar Software Development Doubts
Top Courses for Software DevelopmentView all
The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer?
Question Description
The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer? for Software Development 2024 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Software Development 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer?.
The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer? for Software Development 2024 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Software Development 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer?.
Solutions for The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Software Development.
Download more important topics, notes, lectures and mock test series for Software Development Exam by signing up for free.
Here you can find the meaning of The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.a)630b)540c)450d)360Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Software Development tests.
|
|
Explore Courses for Software Development exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup