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The product of two numbers is 45 and their difference is 4. The sum of squares of the two numbers is
- a)135
- b)240
- c)73
- d)106
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The product of two numbers is 45 and their difference is 4. The sum of...
As we know (a − b)2 = a2 + b2 − 2ab
We assume that first number is a and second number is b hence ab = 45
and a - b = 4
after putting values we will get a2 + b2 = 106
We assume that first number is a and second number is b hence ab = 45
and a - b = 4
after putting values we will get a2 + b2 = 106
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The product of two numbers is 45 and their difference is 4. The sum of...
To solve this problem, we can use a system of equations. Let's call the two numbers x and y.
Given:
The product of two numbers is 45.
xy = 45
Their difference is 4.
x - y = 4
We can solve this system of equations to find the values of x and y.
Solving for x in the second equation:
x = y + 4
Substituting this value of x into the first equation:
(y + 4)y = 45
Expanding and rearranging the equation:
y^2 + 4y - 45 = 0
Now we can factorize the quadratic equation:
(y + 9)(y - 5) = 0
Setting each factor equal to zero and solving for y:
y + 9 = 0 or y - 5 = 0
If y + 9 = 0, then y = -9
If y - 5 = 0, then y = 5
So we have two possible values for y: -9 and 5.
Substituting these values of y back into the equation x = y + 4 to find the corresponding values of x:
If y = -9, then x = -9 + 4 = -5
If y = 5, then x = 5 + 4 = 9
So the two numbers are -5 and 9.
Finding the sum of squares of the two numbers:
(-5)^2 + 9^2 = 25 + 81 = 106
Therefore, the sum of squares of the two numbers is 106, which corresponds to option 'D'.
Given:
The product of two numbers is 45.
xy = 45
Their difference is 4.
x - y = 4
We can solve this system of equations to find the values of x and y.
Solving for x in the second equation:
x = y + 4
Substituting this value of x into the first equation:
(y + 4)y = 45
Expanding and rearranging the equation:
y^2 + 4y - 45 = 0
Now we can factorize the quadratic equation:
(y + 9)(y - 5) = 0
Setting each factor equal to zero and solving for y:
y + 9 = 0 or y - 5 = 0
If y + 9 = 0, then y = -9
If y - 5 = 0, then y = 5
So we have two possible values for y: -9 and 5.
Substituting these values of y back into the equation x = y + 4 to find the corresponding values of x:
If y = -9, then x = -9 + 4 = -5
If y = 5, then x = 5 + 4 = 9
So the two numbers are -5 and 9.
Finding the sum of squares of the two numbers:
(-5)^2 + 9^2 = 25 + 81 = 106
Therefore, the sum of squares of the two numbers is 106, which corresponds to option 'D'.
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The product of two numbers is 45 and their difference is 4. The sum of squares of the two numbers isa)135b)240c)73d)106Correct answer is option 'D'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about The product of two numbers is 45 and their difference is 4. The sum of squares of the two numbers isa)135b)240c)73d)106Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of two numbers is 45 and their difference is 4. The sum of squares of the two numbers isa)135b)240c)73d)106Correct answer is option 'D'. Can you explain this answer?.
The product of two numbers is 45 and their difference is 4. The sum of squares of the two numbers isa)135b)240c)73d)106Correct answer is option 'D'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about The product of two numbers is 45 and their difference is 4. The sum of squares of the two numbers isa)135b)240c)73d)106Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of two numbers is 45 and their difference is 4. The sum of squares of the two numbers isa)135b)240c)73d)106Correct answer is option 'D'. Can you explain this answer?.
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