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      Question

      When the sum of the squares of two positive integers is

      given as 1,600, and their product is given as 768. Determine the value of the smaller integer.
      A 25 Correct Answer Incorrect Answer
      B 24 Correct Answer Incorrect Answer
      C 20 Correct Answer Incorrect Answer
      D 18 Correct Answer Incorrect Answer
      E 15 Correct Answer Incorrect Answer

      Solution

      ATQ, Let, the two numbers be 'm' and 'n', such that, 'm > 'n'. ATQ, m 2 + n2 = 1600 And, m × n = 768 We know that, (a + b)2 = a2 + b2 + 2ab, and, (a - b)2 = a2 + b2- 2ab So, (m + n)2 = 1600 + 2 × 768 Or, (m + n)2 = 1600 + 1536 Or, (m + n)2 = 3136 Since both the numbers are greater than zero. So, m + n = 56 ....(i) Similarly, (m - n)2 = m2 + n2- 2mn So, m - n = 8 ....(ii) On subtracting equation (ii) from equation (i) , we get, 2n = 48 So, n = 24 So, the value of the smaller number = n = 24

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