📢 Too many exams? Don’t know which one suits you best? Book Your Free Expert 👉 call Now!

    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

    Practice Next
    More No. System Questions

    Relevant for Exams:

    ask-question