The minimum value of 1 / A + 1 / B + 2 √ AB is

The minimum value of 1 / A + 1 / B + 2 √ AB is

1/a+1/b+2√ab
=1/a+√ab+1/b+√ab
≥2√(1/a*√ab)+2√(1/b*√ab)
≥2√[2√(1/a*√ab)*2√(1/b*√ab)]
=2*2
=4
That is 1 / A + 1 / B + 2 √ ab ≥ 4
The condition of equal sign is that 1 / a = √ AB, 1 / b = √ AB, 2 √ (1 / A * √ AB) = 2 √ (1 / b * √ AB), that is, a = b = 1
Therefore, when a = b = 1, the minimum value of 1 / A + 1 / B + 2 √ AB is 4

Given that ab > 0, the absolute values of AB are 6 and 8 respectively, find the value of a + B

Because AB > 0, a and B have the same sign, both negative or positive. A + B = 14 or - 14

Given a + B = - 6, ab = 8, find the value of a-b

(a-b)^2
=a^2-2ab+b^2
=a^2+2ab+b^2-4ab
=(a+b)^2-4ab
=(-6)^2-8*4
=36-32
=4
A-B = 2 or A-B = - 2

The square of x plus 10x plus 16 is equal to 0 (with matching method). Now I just add what number I don't know how to choose

The formula needs constant term = (primary term coefficient △ 2) square number to add = original constant term - formula needs constant term x & # 178; + 10x + 16 = x & # 178; + 10x + 25-9 = (x + 5) &# 178; - 9 formula needs constant term = (10 △ 2) square = 25 number to add = 16-25 = - 9. The solution equation is as follows:

X + y divided by 3Y equals the square of x minus the square of Y divided by ()?

3y（x-y）

What is the square of x minus 10x plus 24?

x^2-10x+24
=x^2-4x-6x+24
=(x^2-4x)-(6x-24)
=x(x-4)-6(x-4)
=(x-6)(x-4)

Put the seven numbers 1, 2, 3, 4, 5, 6, 7 in a row "1234567", add the operation symbol "+" in the middle of these numbers, calculate their sum, and the sum is just equal to 100, for example "1 + 23 + 4 + 5 + 67 = 100", can you write a similar formula? Try (be careful not to change the order of the numbers)

1+2+34+56+7=100

Can we fill in "+" - "operation sign and" () "between every two of the 10 natural numbers 1-10 to make the result 48? If so, how many filling methods are there?

No
Because 1 + 2 + 3 ·· + 10 = 55
When one or more "+" is changed to "-", the number is still odd, but 48 is even, so it can't be changed

In 1,2,3,4,5,6,7,8,9,10 these 10 natural numbers between each two arbitrarily fill "+", "-" operation symbols and "()"
In 1,2,3,4,5,6,7,8,9,10 these 10 natural numbers between each two arbitrarily fill "+", "-" operation symbol and "()", and ensure that you can calculate, can make the result 48? If yes, there are several filling methods? If not, please explain the reason

1*2-3+4+5+6+7+8+9+10=48
1+2*3-4+5+6+7+8+9+10=48
1+2+3*4+5-6+7+8+9+10=48
1+2+3+4*5+6+7+8-9+10=48
1-2-3+4+5*6+7-8+9+10=48
1-2-3-4+5+6*7+8-9+10=48
1-2-3-4+5-6+7*8-9+10=48
1-2-3-4-5+6-7+8*9-10=48

In 2012, the 2007 natural numbers add operation symbols by 3 plus 2 minus, then, 6 + 7 + 8-9-10 + 11=

In the first group, 6 + 7 + 8-9-10 + 11 = 2, the second group is equal to 7. In turn, it forms an increasing sequence of equal difference with difference of 5. The five groups are divided into 2007 / 5 quotient 401 groups. The remaining 2 is the last 2011 and 2012. Add the previous 401 groups first. The first 2. The last 2 + 5 * 400 = 2002