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If sum of squares of two real numbers is 12 and the product of the numbers is 4, find the difference between the numbers.
- a)4
- b)8
- c)1
- d)2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If sum of squares of two real numbers is 12 and the product of the num...
Given:
Sum of squares of two numbers = 12,
Product of the numbers = 4
Solution:
Let the numbers be 'a' and 'b'.
ab = 4
Taking the square root of both sides, we get:
a - b = ±2
Therefore, the difference between the numbers is ±2.
Most Upvoted Answer
If sum of squares of two real numbers is 12 and the product of the num...
Understanding the Problem
We have two real numbers, say x and y. We know two key pieces of information:
- The sum of their squares is 12:
x² + y² = 12
- Their product is 4:
xy = 4
Finding the Difference Between the Numbers
To find the difference between x and y, we can use the identity for the square of the difference:
- (x - y)² = (x + y)² - 4xy
First, we need to find x + y. We can derive this from the equations we have.
Step 1: Find x + y
Using the identity:
x² + y² = (x + y)² - 2xy
Substituting the values we know:
12 = (x + y)² - 2(4)
12 = (x + y)² - 8
Now, rearranging gives us:
(x + y)² = 20
Thus, we find:
x + y = √20 = 2√5 (we can keep it in this form for further calculation).
Step 2: Find (x - y)²
Now substituting back into our difference formula:
(x - y)² = (x + y)² - 4xy
(x - y)² = 20 - 16
(x - y)² = 4
Taking the square root gives us:
|x - y| = 2
Thus, the difference between the numbers x and y is 2.
Conclusion
So, the correct answer is option 'D': the difference between the two numbers is 2.
We have two real numbers, say x and y. We know two key pieces of information:
- The sum of their squares is 12:
x² + y² = 12
- Their product is 4:
xy = 4
Finding the Difference Between the Numbers
To find the difference between x and y, we can use the identity for the square of the difference:
- (x - y)² = (x + y)² - 4xy
First, we need to find x + y. We can derive this from the equations we have.
Step 1: Find x + y
Using the identity:
x² + y² = (x + y)² - 2xy
Substituting the values we know:
12 = (x + y)² - 2(4)
12 = (x + y)² - 8
Now, rearranging gives us:
(x + y)² = 20
Thus, we find:
x + y = √20 = 2√5 (we can keep it in this form for further calculation).
Step 2: Find (x - y)²
Now substituting back into our difference formula:
(x - y)² = (x + y)² - 4xy
(x - y)² = 20 - 16
(x - y)² = 4
Taking the square root gives us:
|x - y| = 2
Thus, the difference between the numbers x and y is 2.
Conclusion
So, the correct answer is option 'D': the difference between the two numbers is 2.
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If sum of squares of two real numbers is 12 and the product of the numbers is 4, find the difference between the numbers.a)4b)8c)1d)2Correct answer is option 'D'. Can you explain this answer?
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If sum of squares of two real numbers is 12 and the product of the numbers is 4, find the difference between the numbers.a)4b)8c)1d)2Correct answer is option 'D'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about If sum of squares of two real numbers is 12 and the product of the numbers is 4, find the difference between the numbers.a)4b)8c)1d)2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sum of squares of two real numbers is 12 and the product of the numbers is 4, find the difference between the numbers.a)4b)8c)1d)2Correct answer is option 'D'. Can you explain this answer?.
If sum of squares of two real numbers is 12 and the product of the numbers is 4, find the difference between the numbers.a)4b)8c)1d)2Correct answer is option 'D'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about If sum of squares of two real numbers is 12 and the product of the numbers is 4, find the difference between the numbers.a)4b)8c)1d)2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sum of squares of two real numbers is 12 and the product of the numbers is 4, find the difference between the numbers.a)4b)8c)1d)2Correct answer is option 'D'. Can you explain this answer?.
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