It is known that the discriminant of the equation x & # 178; - (M + 2) x-2n = 0 about X is equal to 0, and x = 1 / 2 is the root of the equation

It is known that the discriminant of the equation x & # 178; - (M + 2) x-2n = 0 about X is equal to 0, and x = 1 / 2 is the root of the equation

Substituting x = 1 / 2 into the equation
(1/2)²-(1/2)(m+2)-2n=0
It's time to tidy up
2m+4=1-8n
m+2=(1-8n)/2
△=0
[-(m+2)]²-4×1×(-2n)=0
(m+2)²+8n=0
[(1-8n)/2]²+8n=0
It's time to tidy up
(8n+1)²=0
n=-1/8
m=(1-8n)/2 -2=(1+1)/2 -2=1-2=-1
m+n=-1 -1/8=-9/8