Question

if lcm of x-a and x-b is x²-2x+1 then values of a and b is​

Answer 1

Answer:If lcm of x-a and x-b is x²-2x+1,then :—(x–a)(x–b)=x²–2x+1Or,x²–ax–bx +ab=x²–2x+1Or,x²–x(a+b)+ab=x²–2x+1On cancellation of x²,we get:—(i)–x(a+b)=–2x (ii) ab=1. ——(2)Or, (a+b)=–2. ——(1) (a+b)=–2 ——(1)Or,(a+b)²=4 [On squaring both sides ]Or,a²+b²+2ab=4Or,a²+b²+2×1=4. [Putting the value of eq. 2]Or,a²+b²=2.Or,a²+b²–2ab=2–2×1=0Or,(a–b)²=0Or,(a–b)=0. ——(3)On adding eq.1 and eq.3 ,we get:—2a=2 Or,a=1.Therefore, b=(2–1)=1.

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