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.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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