The equation x ^ 2 + 2x-3k = 0 has two roots (x1 + 1) (x2 + 1) = - 4 to find K In ten minutes

The equation x ^ 2 + 2x-3k = 0 has two roots (x1 + 1) (x2 + 1) = - 4 to find K In ten minutes

x²+2x-3k=0
So X1 + x2 = - 2
x1x2=-3k
(x1+1)(x2+1)
=x1x2+x1+x2+1
=-3k-2+1=-4
3k=3
k=1

What is the number whose square equals two and one fourth?

2 and 1 / 4 = 2 + 1 / 4 = 9 / 4
Root (9 / 4) = ± 3 / 2

If the variables X, y satisfy the constraint conditions x + Y-3 = 0, Y > = 1, then the maximum value of Z = | y-2x | is 0
A.6
B.5
C.4
D.3

Choose C
It is easy to get that the allowable value range of X and Y is triangle ABC area (including boundary) by combining with graphics
Where a (1,2) B (0,1) C (2,1)
So the value range of X is [0,2], and the value range of Y is [1,2]
From z = | y-2x | we get z = y-2x or Z = 2x-y,
It is easy to get the maximum value of (z = 2-3) where z = 2

Given a ≥ 0, the inequality about X is solved: (AX & sup2; + A & sup2; x-2a) / (AX & sup2; - x + A & sup2; x-a)

When a = 0, the molecule is 0, constant holds, and x0 is OK
a> 0, its denominator = (AX-1) (x + a) = a (x-1 / a) (x + a)
When x > 1 / A or x0, eliminate the denominator and get: X

Solving inequality 12x & # 178; - ax

12x²-ax

Steps of solving inequality 12x ax ＞ a (a ∈ R)=-=

12x-ax-a>0
(3x-a) (4x + a) > 0
One species: 3x-a > 0, 4x + a > 0
x>a/3 x>-a/4
If a ≥ 0, then x > A / 3
If a ≤ 0, then x > - A / 4
2 species: 3x-a

Solving inequality - ax > 2 (a ≠ 0)

－ax＞2
ax＜-2
When a ＞ 0, both sides divide by a, and the direction of unequal sign remains unchanged
x＜-2/a
When a ＜ 0, both sides divide by a, the direction of unequal sign changes
x＞-2/a

12x & # 178; - ax ＞ A & # 178; (a belongs to R) solution inequality

12x²-ax-a²>0
Factorization
(3x-a)(4x+a)>0
The parabolic opening is upward, and the part greater than 0 is on the outside of the two
Two are x = A / 3 and x = - A / 4
When a / 3

Given the set a = [- 2,2], for all real numbers t satisfying the set a, then the value range of inequality x ^ 2 + tx-t > 2x-1 is?

F (x) = (x ^ 2) * (1-x) + (x-1) * t = - x ^ 3 + x ^ 2 + tx-t take the derivative of the above formula F '(x) = - 3x ^ 2 + 2x + T. the function f (x) = AB is an increasing function in the interval (- 1,1). It is shown that f' (x) > = 0 in the interval (- 1,1). Let f '(x) = 0, the solution is x = (1 - √ (1 + 3T)) / 3 and x = (1 + √ (1 + 3T)) / 3

Let a > 0, the solution of the inequality y ^ 2 - (radical a + 1 / radical a) y + 1 is less than or equal to 0
It's due tomorrow

y^2-（√a+1/√a）y+1≤0
That is, (Y - √ a) (Y-1 / √ a) ≤ 0
When a = 1, √ a = 1 / √ a = 1
The original inequality is (Y-1) ² ≤ 0
The solution set of inequality is {1}
When a > 1, √ a > 1 / √ a
The solution set of inequality is [1 / √ a, √ a]
When 0