Question
The least common multiple (LCM) of two numbers is 510,
and their highest common factor (HCF) is 17. Additionally, the sum of these two numbers is 187. Find the sum of the squares of the two numbers.Solution
Let the two numbers be '17a' and '17b'. So, 17a X 17b = 510 X 17 Or, a X b = 30 Given, 17a + 17b = 187 Or, a + b = 11 Required value = (17a)2Â + (17b)2Â = 289(a2Â + b2) We know that (x + y)2Â = x2Â + y2Â + 2xy Or, 112Â = a2Â + b2Â + 2 X 30 Or, 121 - 60 = a2Â + b2 So, a2Â + b2Â = 61 So, required value = 61 X 289 = 17629
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