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let matching number=M , independence number=N , edge cover number=E, vertex cover number =V

given that V-E=2k , M*I=1-2k ----(1)

and we know that V+I=n and M+E=n (n=number of vertices)

V-E=M-I=2k ---(2)

we need M+I

so we know that-- (a+b)^2=(a-b)^2+4ab

(M+I)^2=(M-I)^2+4MI

from eq(1)and (2) (M+I)^2 = 4k^2+4(1-2k)

=4(k^2-2k+1)

=4(k-1)^2

so M+I= 2(k-1)

given that V-E=2k , M*I=1-2k ----(1)

and we know that V+I=n and M+E=n (n=number of vertices)

V-E=M-I=2k ---(2)

we need M+I

so we know that-- (a+b)^2=(a-b)^2+4ab

(M+I)^2=(M-I)^2+4MI

from eq(1)and (2) (M+I)^2 = 4k^2+4(1-2k)

=4(k^2-2k+1)

=4(k-1)^2

so M+I= 2(k-1)