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If \( x \) and \( y \) are any positive integers, then \( \left(x^{2}-x\right)+\left(y^{2}-y\right) \) is always. \( (x \neq 1, y \neq 1) \) (A) even number (B) odd number (C) prime number (D) both even and odd are possible |
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Answer» (x2 - x) + (y2 - y) = x(x - 1) + y(y - 1) = even \(\because\) x(x - 1) is always even for an integer. \(\therefore\) x(x - 1) is even & y(y - 1) is even ⇒ x(x - 1) + y(y - 1) is even ⇒ (x2 - x) + (y2 - y) is even |
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