Q. 33.7( 3 Votes )

If u(x) = (x – 1)

Answer :

u(x) = (x – 1)2

= (x – 1) (x – 1)


v(x) = (x2 – 1)


= (x + 1) (x – 1)


LCM of u(x) and v(x) = (x – 1)2 (x + 1)


HCF of u(x) and v(x) = (x – 1)


u(x) × v(x) = (x – 1) (x – 1) × (x2 – 1)


= (x2 – 2x + 1) × (x2 – 1)


= x4 – 2x3 + x2 - x2 + 2x – 1


= x4 – 2x3 + 2x – 1


HCF × LCM = (x – 1)2 (x + 1) × (x – 1)


= (x2 – 2x + 1) (x2 – 1)


= x4 – 2x3 + x2 - x2 + 2x – 1


= x4 – 2x3 + 2x – 1


So it is observed that HCF × LCM = u(x) × v(x).


Hence Proved.


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