How much is 2 √ 75 + √ 8 - √ 27

How much is 2 √ 75 + √ 8 - √ 27

Simple calculation: 13 / 15 * 2 / 9 + 7 / 15 * 13 / 9

13/15*2/9+7/15*13/9
=13/15*2/9+13/15*7/9
=13/15*(2/9+7/9)
=13/15

1 / 3 = 6 / 15 = 13 / 39 = () 3 / 12 / 5 = 15 / 25 = 125 ()

1 / 3 = 5 / 15 = 13 / 39 = (12 / 36)
3 out of 5 = 15 out of 25 = 75 out of 125

How about 23 times 15 out of 39 plus 15 times 16 out of 39

23*（15/39）+15*（16/39）
=（23*15）/39+（15*16）/39
=(23*15+16*15)/39
=（15*（23+16））/39
=（15*39）/39
=15

Arithmetic sequence (18 21:54:13)
The product cost of an enterprise increases by 20% in the first two years, and decreases by 20% in the next two years after the introduction of advanced technology and equipment. Compared with the original one, the product cost of the enterprise now increases by 8% and decreases by 8% and d by 5%
If there is a convex n-sided shape, the degree of each inner angle forms an arithmetic sequence, the tolerance is 10 degrees, and the minimum is 100 degrees, then the number of edges n = (                   )
If lgx + lgx2 + +Lgx10 = 110, then lgx + lg2x + +lg10x=（                ）

First question: (1 + 20%) ^ 2 * (1-20%) ^ 2 so choose C
Second question: because the minimum angle is 100, so {(100 + 100 + 10n-10) / 2} * n = 180 * (n-2)
So n = 8 or 9
Third question: the former can be reduced to lgx ^ 55 = 55lgx = 110
So lgx = 2
The latter can be reduced to 10lgx + LG10! = LG10! + 20

Exponential function and logarithmic function (31 19:45:58)
Comparison size:
1.1.70.3_____ 0.93.
2. Log root 2 0.5____ Log root 3 root 5 (procedure)
1. The relation between the image of function y = - log5x and y = 5-x is________ .
 

1. Because 1.7 > 1, it is an increasing function of 0.91.7 ^ 0.31

Exponential function (3 14:24:30)
Y = (1 / 3) ^ radical x ^ 2-x + 2, find the range and monotone interval of Y

x^2-x+2
=(x-1 / 2) ^ 2 + 7 / 4 is always greater than 0, so the domain is r
And (x-1 / 2) ^ 2 + 7 / 4 > = 7 / 4
So √ (x ^ 2-x + 2) > = √ 7 / 2
The base 1 / 3 is between 0 and 1
So (1 / 3) ^ x is a decreasing function
So the index > = √ 7 / 2
So y

Arithmetic sequence in senior one
If a ^ 2 B ^ 2 C ^ 2 is equal difference, prove that 1 / B + C 1 / C + a 1 / A + B is also equal difference sequence

1/(b+c)=(a+c)(a+b)/[(a+b)(a+c)(b+c)]
=(a^2+ab+ac+bc)/[(a+b)(a+c)(b+c)]
1/(a+c)=(a+b)(b+c)/[(a+b)(a+c)(b+c)]
=(b^2+ac+bc+ab)/[(a+b)(a+c)(b+c)]
1/(a+b)=(a+c)(b+c)/[(a+b)(a+c)(b+c)]
=(c^2+ab+ac+bc)/[(a+b)(a+c)(b+c)]
2 / (a + C) - [1 / (B + C) + 1 / (a + b)]
=2（b^2+ac+bc+ab)-[(a^2+ab+ac+bc)+(c^2+ab+ac+bc)
=2b^2-(a^2+c^2)
=0 (derived from known conditions)
Therefore, it has been proved

calculation
(1) If {an} is an arithmetic sequence and A1 = 20, an = 54, Sn = 999, find D and n
{1) given equal ratio sequence A1 = - 1, A4 = 64a, find Q and s
{2) given the sequence A1 = - 1, A4 = 64, find Q and S4 to answer the second question. The second question above is wrong

1.an =a1+(n-1)d= 20+(n-1)d=54(n-1)d=34Sn =na1+ nd(n-1)/2 =20n+34n/2=37n=999n = 27d = 34/(27-1) = 17/132.a4 = a1*q^364 = -q^3q = -4s4 = a1(1-q^4)/(1-q) = [(-4)^4 -1]/5 = 51

In the arithmetic sequence {an}, A9 = 15, the first 17 terms and S17=________

a9+a9=a1+a17=2*15=30
s17=1/2 * 17 * (a1+a17)
=1/2*17*30
=255