When k is a value, the equation (K + 1) cos ^ x + 4cosx-4 (k-1) = 0 has real roots

When k is a value, the equation (K + 1) cos ^ x + 4cosx-4 (k-1) = 0 has real roots

Solve this equation
Cosx = 2 (k-1) / (K + 1) or cosx = - 2 (rounding)
-1

The reciprocal of a number is between 1 / 2 and 1 / 4. What is the possible number?
Just one

Three is a quarter

(2 ＋ 3) (2 － 3) if (2x-5) ＋ 4Y ＋ 1 = 0, then x ＋ 2Y = comparison size 3 √ 2
（2＋√3）（2－√3）
If (2x-5) + 4Y + 1 = 0, then x + 2Y = 0
Compare size
3√2 2√3
2 / 2 √ 5-1 1 / 2

(2+√3)(2-√3)=1
2x-5=0,4y+1=0
x=5/2,y=-1/4
x+2y=5/2+2x(-1/4)=2
3√2>2√3
(√5-1)/2>1/2

Let f (x) defined on R satisfy f (x) XF (x + 2) = 13, if f (1) = 2, then f (99) =?

You don't need that multiply sign!
→f(1)=2,f(3)=13/2,f(5)=2,f(7)=13/2
The law is obvious!
Period T = 4, f (x) = f (x + 4)
99=25*4-1
→f(99)=13/2

Let n be a positive integer, 0

We know that n is a positive integer, 0

The quadratic function passes through two points a (- 1,0), B (0, - 3), and the axis of symmetry is x = 1

∵ the parabola passes through the point a (- 1,0), the axis of symmetry is x = 1, and the other intersection of the parabola and the x-axis is (3,0). Let the analytical formula of the parabola be y = a (x + 1) (x-3), and substitute B (0, - 3) to get a = 1, ∵ y = (x + 1) (x-3), that is, y = x2-2x-3

Decompose the factor X & # 178; - 7a & # 178; - 4A & # 178; + 4 in the range of real number

x²-7＝﹙x＋√7﹚﹙x－√7﹚
a²-4a+4＝﹙a－2﹚²

On the equation a (1 + x) &# 178; + 2bx-c (1-x & # 178;) = 0 of X, there are two equal real roots a B C, which are opposite sides of ∠ a ∠ B ∠ C in △ respectively
And SINB = root 2 / 2 to judge the shape of △ ABC

Because the original equation has two equal real roots
So △ = B ^ 2-4ac = 0
So 4B ^ 2-4 (a + C) (A-C) = 0
4b^2-4a^2+4c^2=0
So a ^ 2 = B ^ 2 + C ^ 2
So a triangle with three sides a, B and C is a right triangle
SINB = radical 2 / 2, that is, B / a = radical 2 / 2, so C = B can be obtained by substitution
isosceles right triangle

x+22/8x-22=2/5

x+22/8x-22=2/5
Diagonal multiplication
5(x+22)=2(8x-22)
5x+110=16x-44
16x-5x=110+44
11x=154
x=14

Simplification (X & # 178; - 5) / (x + √ 5)

（X²－5）/（X+√5）
=[（X+√5）（X-√5）]/（X+√5）
=X-√5