Question

Solve the problem 14 given in the pic

Answer 1

{x(x-1)-(m+1)}/{(x-1)(m-1)}=x/m
or, (x²-x-m-1)/(mx-m-x+1)=x/m
or, mx²-mx-m²-m=mx²-mx-x²+x
or, -m²-m=-x²+x
or, x²-x-(m²+m)=0 ------------(1)
Let, α,β are the roots of (1). Then by the given question, α=β.
From the relation between roots and coefficients,
α+β=-(-1/1)=1
or, α+α=1
or, 2α=1
or, α=1/2
α×β=-(m²+m)/1
or, α²=-m²-m
or, (1/2)²=-m²-m
or, 1/4=-m²-m
or, 1=-4m²-4m
or, 4m²+4m+1=0
or, (2m+1)²=0
or, 2m+1=0
or, 2m=-1
or, m=-1/2 (B)