Let Z be the set of all integers andA = {(x, y); x4 – y4 = 175, x, y ∈ Z}B = {(x, y); x > y, x, y ∈ Z}Then, the number of elements in A ∩ B is
Question
Solution 1
To find the number of elements in A ∩ B, we need to find the pairs (x, y) that satisfy both conditions A and B.
Condition A: x^4 - y^4 = 175 Condition B: x > y
First, let's solve the equation x^4 - y^4 = 175. This can be factored into (x^2 - y^2)(x^2 + y^2) = 175.
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