The two intersection coordinates of the straight line y = 3 and the parabola y = - x ^ 2 + 8x-12 are Such as the title

The two intersection coordinates of the straight line y = 3 and the parabola y = - x ^ 2 + 8x-12 are Such as the title

Substituting y = 3 into the parabolic expression, we can get the coordinates as (3,3) (5,3)
(3,3) (5,3)
The square of root 3 + the square of (3-x) = the square of (2Y) becomes the form of y = XXX
The square of root 3 + the square of (3-x) = the square of (2Y) becomes the form of y = XXX
Y = ± (root 3) / (6-2x)
Given function f (x) = ln x-a & # 178; X & # 178; + ax (a ∈ R)
(1) When a = 1, it is proved that the function f (x) has only one zero point
(2) If the function f (x) is a decreasing function in the interval (1, + ∞), find the value range of the real number a
1. When a = 1, f (x) = lnx-x & # 178; + X, the definition field is: x > 0
f'(x)=1/x-2x+1=-(2x²-x-1)/x=-(2x+1)(x-1)/x
x> 0, then: 2x + 1 > 0,
Therefore, it is easy to get: 00 vs. x > 1
If we observe the formula, we can multiply it by a cross
(2ax+1)(ax-1)>0
(1) When a = 0, - 1 > 0, rounding off;
(2) A0, X2 = 1 / A1, then: - 1 / 2A ≤ 1
A ≤ - 1 / 2
So, a ≤ - 1 / 2
(3) When a > 0, X1 = - 1 / 2a0
The solution of the inequality is: X1 / A
For x > 1, then: 1 / a ≤ 1
Results: a ≥ 1
So, a ≥ 1
To sum up, the value range of real number a is: a ≤ - 1 / 2 or a ≥ 1
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Let X1 and X2 be the two roots of the equation 2x Λ 2 + 4x-3 = 0, and use the relationship between the roots and the coefficients to find the values of the following formulas
(1)x2/x1+x1/x2
X1, X2 are the two roots of the equation 2x Λ 2 + 4x-3 = 0
By means of Weida's theorem, it is obtained that:
x1+x2=-2
x1x2=-3/2
Then:
x2/x1+x1/x2
=(x1²+x2²)/x1x2
=[(x1+x2)²-2x1x2]/x1x2
=(4+3)/(-3/2)
=-14/3
Let the coordinates of the intersection of the parabola y = X05 + 8x-4 and the straight line x = 4 be
y=x²+8x-4
The intersection coordinates are (4,44)
Take x = 4 into the equation
Calculation: x + 2Y / X-Y + 2x / y-x-3y / X-Y
Original formula = (x + 2Y) / (X-Y) - 2x / (X-Y) - 3Y / (X-Y)
=(x+2y-2x-3y)/(x-y)
=(-x-y)/(x-y)
The answer is (- 2XY ^ 2-y ^ 2 + 2x ^ 2) / (XY)
a> O, b > O, and the function FX = 4x ^ 3-ax ^ 2-2bx + 2 has an extreme value at x = 1, then the maximum value of AXB is?
F '(x) = 12x ^ 2-2ax-2b substituting x = 1 12-2a-2b = 0 a + B = 6 A + b > = 2 √ ab
Let the root of equation 3x's cubic power - 2x's square + 3x-1 = 0 be x1, X2, X3, and find the value of x1x2 + x2x3 + x1x3
Because x1, X2 and X3 are the three roots of the original equation, the original equation can be written as follows: (x-x1) (x-x2) (x-x3) = 0, which is solved as follows: x ^ 3 - (x1 + x2 + x3) x ^ 2 + (x1x2 + x2x3 + x1x3) x-x1x2x3 = 0, while both sides of the original equation are divided by 3, which is solved as follows: x ^ 3 - (2 / 3) x ^ 2 + X-1 / 3 = 0
Find the intersection coordinates of parabola y = 3x2-8x + 4 and X axis, and make sketch verification
Y = 3x & # 178; - 8x + 4 & nbsp; = & nbsp; (3x-2) (X-2) & nbsp; = & nbsp; 0x & nbsp; = & nbsp; 2 / 3 or X & nbsp; = & nbsp; 2 (2 / 3, & nbsp; 0) and (2, & nbsp; 0)
If 3 / 2Y + x = 8 / 3y-2x = 3, then y = ---, x = ---, 2y-x=-----
y=6, x=-3, 2y-x=15
The answers are 6, - 3 and 15