Question

Find the LCM of xy(k^2+1)+k(x^2+y^2) and xy(k^2-1)+k(x^2-y^2)​

Answer 1

Answer: (ky + x) (k2x2 - y2)

Step-by-step explanation;

Let p(x) = xy(k2 +1) + k(x2 + y2) and

q(x) = xy(k2 −1) + k(x2 −y2)

q(x) = y(k2 −1) + k(x2 −y2)

= xyk2 + ky2 + xy + kx2

= ky(kx + y) + x(y + kx)

p(x) = (ky + x)(kx + y) -----(1)

q(x) = xy(k2 −1) + k(x2 − y2)

q(x) = xyk2 −xy + kx2 − ky2

= xyk2 − ky2 − xy + kx2

= ky(kx - y) + x(kx - y)

= (ky + x)(kx - y) -------(2)

L.C.M = (ky + x)((kx)2 - y2)

L.C.M = (ky + x) (k2x2 - y2)