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  • Question
  • The sum of the square of two numbers is 97 and the square of their difference is 25. The product of the two number is


  • Options
  • A. 45
  • B. 36
  • C. 54
  • D. 63

  • Correct Answer
  • 36 

    Explanation

    Let the two number are a and b
    According to the question
    sum of squares of two numbers = 97
    i.e.., a 2 + b 2 = 97 .....................(i)
    and square of their difference = 25
    i.e., (a - b) 2 = 25 .................(ii)
    ? a - b = 5...............(iii)
    from Eq. (ii)
    a2 + b2 - 2ab = 25
    (a2 + b2) - 2ab = 25
    Now put the value of a 2 + b 2 from Eq. (i)
    ? 97 - 2ab = 25
    ? 2ab = 72
    ? ab = 36.................(iv)
    Now, we have
    (a + b)2 = ( a2 + b2) + 2ab
    Now put the value of a 2 + b 2 from Eq. (i) and ab from Eq. (iv)
    (a + b)2 = 97 + 72 = 169
    a + b = 13.............(v)
    Now add the Eqs. (iii) and (v), we get
    a - b + a + b = 5 +13
    2a = 18
    ? a = 9
    now put the value of a in Eq. (v)
    a + b = 13
    9 + b = 13
    b = 13 - 9
    b = 4
    ? Product of both the numbers = ab = 9 x 4 = 36


  • More questions

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    • B. 131
    • C. 133
    • D. 129
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    • 2. 
      The angle of elevation of the top of a hill from each of the vertices A, B, C of a horizontal triangle is ?. The height of the hill is :

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    • C. c tan ? cosec C 2
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    • 3. 
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    • 4. 
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    • Options
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    • D. 32.72 km/hr.
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    • Options
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