The time required for a ship to sail 66 km downstream is the same as that for a ship to sail 48 km upstream. Given the current velocity of 3 km / h, if the distance between AB and ab docks is 44 km, the time required for a ship to go back and forth is calculated

The time required for a ship to sail 66 km downstream is the same as that for a ship to sail 48 km upstream. Given the current velocity of 3 km / h, if the distance between AB and ab docks is 44 km, the time required for a ship to go back and forth is calculated

Set ship speed x
66/(x+3)=48/(x-3)
66x-198=48x+144
18x=342
x=19
44/(19+3)+44/(19-3)=2+2.75=4.75

It is known that the univariate quadratic equation x ^ 2 - (m ^ 2 + 3) x + 1 / 2 (m ^ 2 + 2) = 0
1. Proof: no matter what the value of M is, the equation has two positive roots,
2. Let X1 and X2 be two of the equations, and satisfy X1 ^ 2 + x2 ^ 2 - x1x2 = 17 / 2, find the value of M

1) First of all, there are roots,
△=b^2-4ac
=(m^2+3)^2-2(m^2+2)
=m^4+4m^2+5
=(m ^ 2 + 2) ^ 2 + 1 > 0 no matter what the value of M is greater than 0
No matter what the value of M is, the equation has two unequal real roots,
Two are x1, x2,
x1+x2=m^2+3>0,
x1*x2=(m^2+2)/2>0
So no matter what real number m takes, the equation has two positive roots
2）a^+b^2-ab=17/2,
（a+b）^2-3ab=17/2,
(m^2+3)^2-3(m^2+2)/2=17/2,
2m^4+9m^2-5=0,
(2m^2-1)(m^2+5)=0
M ^ 2 + 5 is not 0, so 2m ^ 2-1 = 0,
m=ñ2/2

If a is the root of the equation x2-3x + 1 = 0, find 2a2-5a-2 + 3a2 + 1=______ ．

∵ A is the root of the equation x2-3x + 1 = 0, ∵ a2-3a + 1 = 0, ∵ A2 + 1 = 3A, ∵ a + 1A = 3, ∵ 2a2-5a-2 + 3a2 + 1 = 2a2-6a + A-2 + 3a2 + 1 = - 2-2 + A + 1A = - 1, so the answer is: - 1