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Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164.​
  • a)
    14 and 2
  • b)
    11 and 5
  • c)
    12 and 4
  • d)
    10 and 6
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Divide 16 into two parts such that twice the square of the larger part...
Let x and (16 - x) are two parts of 16 where (16 - x) is longer and x is smaller .
A/C to question, 
2 * square of longer = square of smaller + 164 
⇒ 2 * (16 - x)^2 = x^2 + 164 
⇒ 2 * (256 + x^2 - 32x ) = x^2 + 164 
⇒ 512 + 2x^2 - 64x = x^2 + 164 
⇒ x^2 - 64x + 512 - 164 = 0
⇒ x^2 - 64x + 348 = 0
⇒x^2 - 58x - 6x + 348 = 0
⇒ x(x - 58) - 6(x - 58) = 0
⇒(x - 6)(x - 58) = 0
⇒ x = 6 and 58 
But x ≠ 58 because x < 16 
so, x = 6 and 16 - x = 10 
Hence, answer is 6 and 10
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Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164.​a)14 and 2b)11 and 5c)12 and 4d)10 and 6Correct answer is option 'D'. 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 Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164.​a)14 and 2b)11 and 5c)12 and 4d)10 and 6Correct answer is option 'D'. 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 Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164.​a)14 and 2b)11 and 5c)12 and 4d)10 and 6Correct answer is option 'D'. Can you explain this answer?.
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