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The sum of the squares of three consecutive positive numbers is 365. What will the sum of numbers?
- a)36
- b)33
- c)45
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The sum of the squares of three consecutive positive numbers is 365. W...
Problem Analysis
We are given that the sum of the squares of three consecutive positive numbers is 365. Let's assume the three consecutive numbers as x, x+1, and x+2.
Solution
We can represent the sum of the squares of these three numbers as an equation:
x^2 + (x+1)^2 + (x+2)^2 = 365
Expanding the equation:
x^2 + (x^2 + 2x + 1) + (x^2 + 4x + 4) = 365
3x^2 + 6x + 5 = 365
3x^2 + 6x - 360 = 0
Divide the equation by 3:
x^2 + 2x - 120 = 0
Factorizing the Equation
We need to factorize the quadratic equation x^2 + 2x - 120 = 0 to find the values of x.
(x + 12)(x - 10) = 0
From the equation, we have two possible values for x:
x + 12 = 0 or x - 10 = 0
If x + 12 = 0, then x = -12, which is not a positive number. Hence, we discard this solution.
If x - 10 = 0, then x = 10. This gives us the first number as 10.
Calculating the Other Numbers
Using the value of x = 10, we can calculate the other two consecutive numbers:
First number: x = 10
Second number: x + 1 = 10 + 1 = 11
Third number: x + 2 = 10 + 2 = 12
Sum of the Numbers
The sum of the three numbers is:
10 + 11 + 12 = 33
Therefore, the correct answer is option 'B', which is 33.
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Community Answer
The sum of the squares of three consecutive positive numbers is 365. W...
Suppose the three consecutive positive numbers be x, x + 1, and x + 2
According to the question,
(x)2 + (x + 1)2 + (x + 2)2 = 365
On expanding, we will get,
x2 + x2 + 1 + 2x + x2 + 4 + 4x = 365
3x2 + 6x = 360
Or, x2 + 2x - 120 = 0
=> (x - 10) (x + 12) = 0
So, x = 10
First number x = 10
Second number x + 1 = 11
Third number x + 2 = 12
So, sum of the numbers is = 10 + 11 + 12 = 33
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The sum of the squares of three consecutive positive numbers is 365. What will the sum of numbers?a)36b)33c)45d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The sum of the squares of three consecutive positive numbers is 365. What will the sum of numbers?a)36b)33c)45d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the squares of three consecutive positive numbers is 365. What will the sum of numbers?a)36b)33c)45d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
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