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Question
Find the least common multiple of xy(k2 + 1) + k(x2 + y2) and xy(k2 – 1) + k(x2 – y2)
Solution
xy(k2 + 1) + k(x2 + y2) ...(1)
xy(k2 – 1) + k(x2 – y2) ...(2)
(1) ⇒ xyk2 + xy + kx2 + ky2
(2) ⇒ xyk2 – xy + kx2 – ky2
(1) ⇒ yk (xk + y) + x (xk + y)
= (xk + y) (x + yk)
(2) ⇒ yk (xk – y) + x (xk – y)
= (x + yk) (xk – y)
∴ L.C.M. : (x + yk) (xk + y) (xk – y)
= (x + yk) (x2k2 – y2)
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