When the sum of the squares of two positive integers is

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