This year, Xiaodong's father is four times as old as Xiaodong's. 20 years later, Xiaodong's father is two times as old as Xiaodong's. how old are Xiaodong and his father this year?

If my father is 4x years old this year, Xiaodong is x years old
20 years later, 4x + 20 = 2 * (x + 20), x = 10
So, dad is 40 years old and Xiaodong is 10 years old

Why should X be all real numbers when using discriminant method to find value range?

(2) Let y = X-2 / X (2) + 1 (formula 1) require the range of Y. The reason why the root formula can be used is that x is any real number, which is equivalent to the constant solution of X in the equation. On the contrary, if x is not any real number, that is to say, there is no constant solution in Formula 1, the root formula can not be used

Xiao Ming and his father are 34 years old now. Three years later, his father is 24 years older than Xiao Ming. How old are Xiao Ming and his father this year?

Let Xiaoming's age be x years old, then the father's age is: (x + 24) years old, x + 24 + x = 34, & nbsp; 2x + 24 = 34, & nbsp; & nbsp; 2x = 10, & nbsp; & nbsp; & nbsp; & nbsp; X = 5; the father's age is: 24 + 5 = 29. A: Xiaoming is 5 years old, father is 29 years old

Using discriminant method to find function range

This method is suitable for fractional function, the highest order term is twice, numerator and denominator can't be reduced
For example: y = x / (x ^ 2 + 1)
If we take x as the unknown and y as the coefficient, we can change it into equation form
yx^2-x+y=0
This equation must have a solution, because the domain of definition of the function must be nonempty. Therefore, the discriminant = 1-4y ^ 2 > = 0
The solution to the inequality is that the range is
－0.5

Xiao Ming and his father are 34 years old now. Three years later, his father is 24 years older than Xiao Ming. How old are Xiao Ming and his father this year?

First, write the solution
Let Xiaoming's age be x and dad's age be y
x+y=34
x+24=y
x+24-24=y-24
x=5
34-5 = 29 A: Xiao Ming is 5 years old and his father is 29 years old

Function to find the range of y = (x ^ 2 + 1) / x, x > = 2, can we use the discriminant method?

For the function y = x + 1 / X (x ≥ 2)
∵ y = x + 1 / x increases monotonically on X ≥ 2, so the minimum value of y = 5 / 2 is obtained when x = 2, and tends to infinity when x tends to infinity
The value range is 5 / 2 ≤ y
Can use discriminant method, the conclusion is the same, the process is more cumbersome

Xiao Ming and his father are 34 years old now. Three years later, his father is 24 years older than Xiao Ming. How old are Xiao Ming and his father this year?

The range of function y = - 3x ^ 2 + 6x + 5 is

Method 1
According to the meaning of the title:
Function definition field is R (rational number)
Because the coefficient of quadratic term is less than 0
-3 < 0
So the function has a maximum value:
(4ac-b^2)/4a = 8
So the range is: (- ∞, 8]
Or write X

Xiao Ming and his father are 34 years old now. Three years later, his father is 24 years older than Xiao Ming. How old are Xiao Ming and his father this year?

Three years later, my father is 24 years older than Xiao Ming. How old is my father now? He is 24 years older than Xiao Ming!
So: (34-24) △ 2 = 5 years old Xiao Ming is five years old now
34-5 = 29 years old Dad is 29 now

To find the range of y = 6x + 1 + 2 √ 3x-1, let t = √ 3x-1 be 2 (T + 1 / 2) ^ 2 + 5 / 2 by the method of substitution
So why is the range written from 3 to positive infinity?

t=√3x-1
So t > = 0
On the right side of the symmetry axis t = - 1 / 2
So t = 0, the minimum is 3

This year, Xiaodong's father is four times as old as Xiaodong's. 20 years later, Xiaodong's father is two times as old as Xiaodong's. how old are Xiaodong and his father this year?