if lcm of x-a and x-b is x²-2x+1 then values of a and b is
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if lcm of x-a and x-b is x²-2x+1 then values of a and b is
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Answer:
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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.