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The sum of the squares of two consecutive positive odd numbers is 290. Find the sum of the numbers :
- a)14
- b)24
- c)28
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The sum of the squares of two consecutive positive odd numbers is 290....
Let one of the odd positive integer be x
then the other odd positive integer is x+2
their sum of squares = x² +(x+2)²
= x² + x² + 4x +4
= 2x² + 4x + 4
Given that their sum of squares = 290
⇒ 2x² +4x + 4 = 290
⇒ 2x² +4x = 290-4 = 286
⇒ 2x² + 4x -286 = 0
⇒ 2(x² + 2x - 143) = 0
⇒ x² + 2x - 143 = 0
⇒ x² + 13x - 11x -143 = 0
⇒ x(x+13) - 11(x+13) = 0
⇒ (x-11) = 0 , (x+13) = 0
Therfore , x = 11 or -13
We always take positive value of x
So , x = 11 and (x+2) = 11 + 2 = 13
Therefore , the odd positive integers are 11 and 13 .
then the other odd positive integer is x+2
their sum of squares = x² +(x+2)²
= x² + x² + 4x +4
= 2x² + 4x + 4
Given that their sum of squares = 290
⇒ 2x² +4x + 4 = 290
⇒ 2x² +4x = 290-4 = 286
⇒ 2x² + 4x -286 = 0
⇒ 2(x² + 2x - 143) = 0
⇒ x² + 2x - 143 = 0
⇒ x² + 13x - 11x -143 = 0
⇒ x(x+13) - 11(x+13) = 0
⇒ (x-11) = 0 , (x+13) = 0
Therfore , x = 11 or -13
We always take positive value of x
So , x = 11 and (x+2) = 11 + 2 = 13
Therefore , the odd positive integers are 11 and 13 .
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The sum of the squares of two consecutive positive odd numbers is 290. Find the sum of the numbers :a)14b)24c)28d)None of theseCorrect answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The sum of the squares of two consecutive positive odd numbers is 290. Find the sum of the numbers :a)14b)24c)28d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the squares of two consecutive positive odd numbers is 290. Find the sum of the numbers :a)14b)24c)28d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
The sum of the squares of two consecutive positive odd numbers is 290. Find the sum of the numbers :a)14b)24c)28d)None of theseCorrect answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The sum of the squares of two consecutive positive odd numbers is 290. Find the sum of the numbers :a)14b)24c)28d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the squares of two consecutive positive odd numbers is 290. Find the sum of the numbers :a)14b)24c)28d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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