If x / x ^ 2-x + 1 = 6 / 7, find x ^ 4 + x ^ 2 + 1 / x ^ 2

If x / x ^ 2-x + 1 = 6 / 7, find x ^ 4 + x ^ 2 + 1 / x ^ 2

(x²-x+1)/x=7/6
x -1 +1/x=7/6
∴x+1/x=13/6
Two sides square
x²+2+1/x²=169/36
x²+1+1/x²=133/36
∴（x^4+x^2+1)/x^2=133/36

The solution equation: (X-2) (x + 1) (x + 4) (x + 7) = 19

Let y = (x2 + 5x − 14) + & nbsp; (x2 + 5x + 4) & nbsp; & nbsp; 2 = x2 + 5x-5, then (Y-9) (y + 9) = 19, that is, y2-81 = 19. The solution is y1.2 = ± 10. Substituting the values of Y1 and Y2 into formula ①, x1.2 = − 5 ± 852, x3.4 = − 5 ± 52,

Experimental report on Design of sinusoidal AC circuit and improvement of power factor
This experiment is a design experiment, which is required to be written according to the design experiment

Add capacitive compensation to measure inductance

Given the set a = {1,2,3,4} B = {3,4,5,6,7} C = {6,7,8,9}, find (1) a ∩ B a ∩ B ∩ C (2) a ∪ B a ∪ B ∪ C
The known set a = {1,2,3,4} B = {3,4,5,6,7} C = {6,7,8,9}
Find (1) a ∩ B a ∩ B ∩ C
（2）A∪B A∪B∪C

1
A∩B={3,4}
A∩B∩C={ø}
two
A∪B={1,2,3,4,5,6,7}
A∪B∪C={1,2,3,4,5,6,7,8,9}

As shown in the figure, AC = half of CD, e is the midpoint of BD, de = one fifth, ab = 2cm, find the length of CE

De = 1 / 5ab = 2cm, e is the midpoint of BD
BD=2DE=2×2=4cmAB=10cm
Ad = ab-de = 6cm ∵ AC = 1 / 2CD, that is CD: AC = 2:1
CD=6÷(2+1)×2=4cm∴CE=CD+DE=4+2=6(cm)

Let a and B be square matrices of order n, and I be identity matrix of order n. if a + B = AB, ab = Ba is proved

A + B = AB, so (A-I) (B-I) = I. It shows that A-I and B-I are inverse matrices. Let them be x, y,
That is, a = I + X, B = I + y, X and y are inverse,
So AB = (I + x) (I + y) = I + X + y + xy = 2I + X + y,
BA=(I+Y)(I+X)=2I+X+Y,
AB=BA

Judge the position relationship between the line and the circle and write the process. The line x + y = 2 and the circle X & # 178; + Y & # 178; = 2 write the process. Thank you

y=2-x
x^2+(2-x)^2=2
2x^2-4x+2=0
x^2-2x+1=0
The discriminant 4-4 = 0 is tangent

Calculation of higher definite integral ∫ (x-xsinx) DX

Partial integral
∫ x dx - ∫ xsinx dx =1/2X^2 + xcosx - sinx

How to divide the eight numbers 6,4,8,22,30,21,35,33 into two groups so that the product of four numbers in each group is equal

6
four
8=2*4
22=2*11
30=6*5
21=3*7
35=5*7
33=3*11
The two groups were divided into two groups
35,33,6,8
21,30,22,4

One third of the boys and one fourth of the girls are 13, and one fourth of the boys and one half of the girls are 16. How many boys and girls are there?

One third of the boys and one fourth of the girls are 13, and two thirds of the boys and two quarters of the girls are 13 × 2 = 26
The number of male students; (26-16) / (2 / 3-1 / 4) = 10 / 5 / 12 = 24,
The number of female students: (16-24 × 1 / 4) △ 1 / 2 = 10 △ 1 / 2 = 20