It is known that a is a root of the quadratic equation x2-5x + 1 = 0, and the value of A2 + 1A2 is obtained

It is known that a is a root of the quadratic equation x2-5x + 1 = 0, and the value of A2 + 1A2 is obtained

Substituting x = a into the equation: a2-5a + 1 = 0, that is, a + 1A = 5, the square of both sides is: (a + 1a) 2 = A2 + 1A2 + 2 = 25, then A2 + 1A2 = 23
Under what circumstances does the discriminant of quadratic equation with one variable have two opposite roots
ax^2+bx+c=0
There are two opposite roots
Then X1 + x2 = 0
Because X1 + x2 = - B / A
So B = 0
B = 0 and ac0 has no real root at all)
The discriminant of the equation is greater than 0 and C / a = 1
Under what circumstances does the discriminant of quadratic equation with one variable have two opposite roots
x1=-x2
x1+x2=0=-b/(2a) b=0
x1*x2=-(b^2-4ac)/(4a)=c=-X1^2
If one root of the equation x ^ 2 + X + a = 0 about X is greater than 1 and the other root is less than 1, the value range of real number a is obtained
y=x²+x+a
The opening is upward, and the intersection point of X axis is on both sides of x = 1
So when x = 1, y is below the x-axis
That is, x = 1
y=1+1+a
It is known that the square + 4x + m of the equation x is equal to one root of 0, which is twice of the other root. Find the two roots of the equation and the value of M
Let two be x1, 2x1
Then we can know from the relationship between root and coefficient
x1+2x1=-4
3x1=-4
x1=-4/3 2x1=-8/3
And X1 * 2x1 = m
M=(-4/3)*(-8/3)
=32/9
x1+x2=-4
x1=2x2
So X1 = - 8 / 3, X2 = - 4 / 3. M = x1x2 = 32 / 9.... thank you..
Why there is only one solution to the system of linear equations of two variables
Binary linear equations can be reduced to the form of y = KX + B, so when there is one solution of binary linear equations, two lines intersect, which is also the most common case. It is also possible that two lines are parallel, then the equations have no solution. For example, when y = x, y = x + 1 are combined, the equations have no solution. The last case is that two lines coincide, and the equations have countless solutions
Let's say that the quadratic equation of two variables is a straight line in coordinates, so there is only one intersection point between X, y and coordinates
Because the system of linear equations of two variables (whether it is substituted into elimination or addition and subtraction elimination) can eventually be transformed into a linear equation of one variable, so there is only one solution.
I think it can be adopted!
There are many special solutions
。。。 Because there are only two variables of degree one in the equation of degree two... The two equations of binary linear equations limit the relationship between them, so there is only one solution..
When m is sum, the square of the equation x minus 4x plus m minus 1 equals 0?
Question 1 has two unequal real roots, question 2 has an equal real root, and question 3 has no real root
The discriminant of x ^ 2-4x + M-1 = 0 root 16-4 (m-1) when 16-4 (m-1) > 0, that is, when M5, there is no real root
What skills do you have for solving linear equations of two variables
Observation is very important. Through observation, you can decide whether to use addition and subtraction elimination or substitute elimination. When you do some difficult equations, the effect of observation is the most obvious. If you do the problem without observation, it will not only take time, but also can not get full marks even if you do it right. If you find the characteristics of the equations through observation, what are the problems
The equation (2Y + 1) (3y-2) = y & # 178; + 2 is reduced to a general form
（2y+1)(3y-2）=y²+2
6y²+3y-4y-2=y²+2
6y²+3y-4y-2-y²-2=0
5y²-y-4=0
（2y+1)(3y-2）=y²+2
6y^2-4y+3y-2-y^2-2=0
5y^2-y-4=0
6Y2－Y－2＝y2+2
5y2-y-4=0
（y-1）（5y+4）=0
y=1,y=-0．8
The formula of pursuit and encounter (middle school)
Encounter problem
Encounter distance = speed and X encounter time
Encounter time = encounter distance △ speed and
Speed sum = encounter distance △ encounter time
Follow up questions
Pursuit distance = speed difference × pursuit time
Pursuit time = pursuit distance △ speed difference
Speed difference = pursuit distance △ pursuit time
① If a is a positive integer, then the integer root of the equation x ^ 2 + 3x + a = 0 is_____ (2) solve the equation: 1 / 2 (3x + 1) ^ 2 = 4 (3) 2x ^ 2-2 times root sign 3x + 1 = 0
① If a is a positive integer, then the integer root of the equation x ^ 2 + 3x + a = 0 is___ 2__ .
② Solution equation: 1 / 2 (3x + 1) ^ 2 = 4
(3x+1)^2=8
3x + 1 = ± 2 pieces 2
X1 = (- 1 + 2 root 2) / 3 x2 = (- 1-2 root 2) / 3
③ 2X ^ 2-2x radical 3x + 1 = 0
X = (2 3 ± 12-8)) / 4
=(2 pieces 3 ± 2) / 4
X1 = (root 3 + 1) / 2 x2 = (root 3-1) / 2