Question
The cube of the difference between two given natural
numbers is 1000, while the product of these two given numbers is 56. Find the positive difference between the cubes of these two given numbers.Solution
1st natural number = x 2nd natural number = y (x - y)3 = 1000 (x - y) = 3√1000 = 10        … (1) squaring both sides  (x - y) ² = 100 x2+y2-2xy =100 x² + y² = 100 + 112 = 212 Now, (x + y) = √ (x² + y² + 2xy) =√ (212 + 112) = √324 = 18 … (2) Now Eq (1) +Eq (2). x-y+x+y =10+18=28 2x =28 x=14 y=4 Now positive difference between the cubes= (14)3-(4)3 =2744-64 =2680.
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