The difference between the squares of two numbers is 256000 and the sum of the numbers is 1000. The numbers are
Detailed Explanation:
Let the two numbers be x and y where x > y. Given: x² - y² = 256000 and x + y = 1000.
Using the identity x² - y² = (x + y)(x - y), we get 256000 = 1000(x - y), hence x - y = 256. Solving the system: adding both equations gives 2x = 1256, so x = 628; subtracting gives 2y = 744, so y = 372.
Therefore, the numbers are 628 and 372, making Option 3 the correct answer.
Question 8 of 8 Number System
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If n is any positive integer, then (34n−43n) is always divisible by
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