Question

if the L.C.M of (x-a) and (x-b) is x²-2x+1 then the value of a and b.

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Answer 1

Step-by-step explanation:

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

Answer 2

Answer:

a = 1 and b = 1

Step-by-step explanation:

lcm of (x-a) and (x-b) = x²-2x+1

so, (x-a) (x-b) = x²-2x+1

x²-ax-xb+ab = x²-2x+1

-ax-xb+ab = -2x+1

-(a+b)x+ab = -2x+1

comparing,,,

a+b = 2

and ab = 1 => b = 1/a

so, a+1/a = 2

a²+1 = 2a

a²-2a+1 = 0

a²-a-a+1 = 0

a(a-1)-1(a-1) = 0

(a-1) (a-1) = 0

so, a = 1

and b = 1 .... ans.