The square of X - 5x + 7 formula

The square of X - 5x + 7 formula

X & # 178; - 5x + (5 / 2) & # 178; - (5 / 2) & # 178; + 7 = (X-5 / 2) & # 178; + 0.75

Monotone interval of function y = 2x square-5x-3

y=2x²-5x-3
=2（x²-5/2x)-3
=2(x²-5/2+25/16)-3-25/8
=2(x-5/4)²-49/8
When x ∈ (- ∝, 5 / 4], it decreases monotonically
When (5 / 4, + ∝), it increases monotonically

The monotone increasing interval of F (x) = 5x ^ 2-2x is f (x) = 5x^

f(x)=5x^2-2x
=5(x^2-2x/5+1/25)-1/5
=5(x-1/5)^2-1/5
Because 5 > 0
So the increasing interval is [1 / 5, + ∞)

To solve the equation: 1 / 3x + 3 / 8x = 1 / 6 fast,

1/3x+3/8x=1/6
17/24x=1/6
x=1/6÷17/24
x=4/17
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Calculation (1-1 / 50) (1-1 / 49) (1-1 / 48); (1-1 / 4) (1-1 / 3) (1-1 / 2) =?

(1－1／50)(1－1／49)(1－1／48).(1-1/4)(1-1/3)(1-1/2)
=49/50*48/49*47/48*.*3/4*2/3*1/2
=1 / 50 (the same numerator and denominator are offset)

If the value range of function f (x0) on [M, n] is [M, n], find the value range of real number a

The title is not complete, help you to complete:
Given the function f (x) = 1 / A-1 / X (a > 0, x > 0). (1) if the range of F (x) on [M, n] is [M, n], find the value range of a, and find the corresponding value of M, n. (2) if f (x) is less than or equal to 2x, it is constant on (0, + infinity), find the value range of A
(1) Let 00, so the range of a is 0

Find the remainder of the product 418 * 811 * 1616 divided by 13

418 divided by 13, the remainder is 2
811 divided by 13, the remainder is 5
1616 divided by 13 is 4
So 418 * 811 * 1616 divided by 13 is equal to 2 * 5 * 4 divided by 13
2 * 5 * 4 = 40 divided by 13, the remainder is 1
So the remainder of 418 * 811 * 1616 divided by 13 is 1

(9 / 8-1 / 4 + 5 / 6) △ 1 / 36 simple calculation
(9/8-1/4+5/6)÷1/36 3/8÷（3/4-1/8） （2-0.6）÷7/15 23×17/24 2/7+5/7×7/15

Given that the ellipse 3x & # 178; + 4Y & # 178; = 12, try to determine the value range of M, so that for the straight line L: y = 4x + m, there are two different points a and B on the ellipse symmetrical about the straight line

Let y = - 1 / 4x + n be the line of a and B
3x & # 178; + 4Y & # 178; = 12 and y = - 1 / 4x + n eliminate y simultaneously, then y is obtained
13x^2-8nx+16n^2-48=0
Let AB (x1, Y1), (X2, Y2), AB midpoint m (x ', y')
x1+x2=8n/13 ,x1x2=(16n^2-48)/13
x'=4n/13,y'=-n/13+n=12n/13
Δ=64n^2-52(16n^2-48>0
n^2

If the inequality system X ≤ MX > 11 has no solution, then the range of M is______ ．

Because the system of inequalities x ≤ MX ＞ 11 has no solution, according to the "large and small solutions can not" so m ≤ 11. So the answer is m ≤ 11