Question

If the l.c.m. of (x - a) and (x - b) is x^2 - 2x + 1, then the value of a and b respectively are

Answer 1

Given H.C.F,L.C.M of two expressions as (x+1)(x

2

+6x+8),(x+1).Let the expressions be a,b.

If a,b are two numbers and their H.C.F,L.C.M are c,d then we know that a×b=c×d.

Using this we can conclude that ;

a×b=(x+1)

2

(x

2

+6x+8)

given one of the a,b is (x

2

+3x+2)=(x+1)(x+2)

(x+1)

2

(x

2

+3x+2)=(x+1)

2

(x+2)(x+4)

=[(x+1)(x+2)(x+1)][(x+4)]

=[x

2

+3x+2][x

2

+5x+4]

hence the other expression is x

2

+5x+4