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Question 15
If $$x$$ and $$y$$ are natural numbers such that $$x + y = 2017$$, then what is the value of $$(- 1)^x + (- 1)^y$$?
Solution
x+y =2017
Now x and y are natural numbers
Now as 2017 is odd number
we know that for the sum of two numbers to be odd
one has to be even and other has to be odd
so we can say always one of x and y will be odd and the other will be even for their sum to be 2017
Now (-1) raised to even = 1 and (-1) raised to odd = -1 so always this will cancel each other and sum will be 0
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