If the solution of the equation 4x-m = 2x-4-5m about X is negative, then the value range of M is ()

If the solution of the equation 4x-m = 2x-4-5m about X is negative, then the value range of M is ()

4x－2x=m－4－5m
2x=－4－4m
x=－2－2m
Because x

Try to determine the value of m so that the equation 4x + (m-2) + m-5 = 0 is negative

Three conditions
1. The discriminant is greater than or equal to 0
2. The product is greater than 0
3. The sum of two is less than 0
(m-2)²-16(m-5)>=0 (1)
(m-5)/4>0 (2)
-(m-2)/45
From (3), M > 2
∴5

Given that M is a root of the equation x ^ 2-3x + 1 = 0, find the value of the fraction m ^ 2-2m + 3 / (m ^ 2 + 1)

Because x ^ 2-2x = X-1
So m ^ 2-2m = M-1
Similarly, 3 / (m ^ 2 + 1) = 3 / 3M = 1 / M
And X is not equal to 0, so x-3 + 1 / x = 0, that is, x + 1 / x = 3
Original formula = X-1 + 1 / x = x + 1 / X-1 = 3-1 = 2

Given that M is a root of the equation x-3x + 1 = 0, find the value of m-2m + m + 3 / 1

M is a root of the equation x ^ 2-3x + 1 = 0
m^2-3m+1=0
m≠0
m+1/m=3
m^2-2m=m-1
m^2+1=3m
m^2-2m+3/(m^2+1)
=m-1+3/3m
=m+1/m-1
=3-1
=2