If the natural numbers x and y satisfy the equation x2 - xy - 101 = 0, then which of the following is a possible value of (x + y)?a)100b)101c)200d)201Correct answer is option 'D'. Can you explain this answer?

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If the natural numbers x and y satisfy the equation x² - xy - 101 = 0, then which of the following is a possible value of (x + y)?

a)
100
b)
101
c)
200
d)
201

Correct answer is option 'D'. Can you explain this answer?

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If the natural numbers x and y satisfy the equation x2 - xy - 101 = 0,...

We simplify the equation x²- xy - 101 = 0 as, x(x- y) = 101 = 1 * 101. As x and y are integers, we have, x = 1 and x - y = 101, or x = 101 and x - y = 1.
If x = 1 , y = 1 - 101 = -100.
If x = 101 , y = 101 - 1 = 100.

As x and y are natural numbers, we must disregard the solution (x, y) = (1, - 100).
There is only one solution: x = 101 and y = 100.
For this set, we have (x + y) = 101 + 100 = 201.
Hence, option 4.

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If the natural numbers x and y satisfy the equation x2 - xy - 101 = 0, then which of the following is a possible value of (x + y)?a)100b)101c)200d)201Correct answer is option 'D'. Can you explain this answer?

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