Question
The cube of the difference between two given natural
numbers is 1728, while the product of these two given numbers is 108. Find the sum of the cubes of these two given numbers.Solution
1st natural number = x 2nd natural number = y (x - y)3 = 1728 (x - y) = 3√1728 = 12 squaring both sides  (x - y) ² = 144 x2+y2-2xy =144 x² + y² = 144 + 216 = 360 Now, (x + y) = √ (x² + y² + 2xy) =√ (360 + 216) = √576 = 24 (x + y) ³ = x³ + y³ + 3xy x (x + y) x³ + y³ = (x + y) ³ -3xy × (x + y) = (24)3 - 3 x 108 x 24 =13824-7776 = 6048
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