-What is x + 5 = 2 / 3x?

-What is x + 5 = 2 / 3x?

-5/3x=-5 x=3

2X plus 3x equals 30, x equals several

6

How much is (- x) multiplied by (2x squared-3x-1)

-2x 3 +3x 2 +x

Sequence an, A1 = 2, an = 2A (n-1) + 2n times (n ≥ 2)
(1) Proving that the sequence an / 2n is an arithmetic sequence
(2) Finding the first n terms and Sn of sequence an
(3) If BN = 2N-1 / an, it is proved that BN is a decreasing sequence

a1+2a2+3a3+… +nan=（n-1）sn+2n（n€N*）
(1) First, A1
n=1,
∴ a1=2
(2) Using the recursive formula:
∵ a1+2a2+3a3+…… +(n-1)a(n-1)+nan=(n-1)Sn+2n ①
∴ a1+2a2+3a3+…… +(n-1)a(n-1) =(n-2)S(n-1)+2(n-1) ②
①-②：
nan =(n-1)Sn-(n-2)S(n-1)+2n
That is n [S (n) - S (n-1)] = (n-1) Sn - (n-2) s (n-1) + 2
∴ S(n)=2S(n-1)+2
∴ S(n)+2=2[S(n-1)+2]
{Sn + 2} is an equal ratio sequence with S1 + 2 = 2 + 2 = 4 as the first term and 2 as the common ratio,
∴ Sn+2=4*2^n=2^(n+1)
∴ Sn=-2+2^(n+1)
When n ≥ 2, an = SN-S (n-1) = 2 ^ (n + 1) - 2 ^ (n) = 2 ^ n
N = 1 also satisfies the above equation
∴ an=2^n
Are you satisfied with the above answers?

For a room, 128 pieces of 5-decimeter-long square bricks are needed. How many pieces of 8-decimeter-long square bricks do you need
Use proportion!

Suppose: X blocks are needed
5×5×128=8×8x
25×128=64x
3200=64x
50=x

7:4.8 108:36

1:7:4.8
=16/9:24/5
=16*5:9*24
=10:27
108：36
=108÷36:36÷36
=3:1

Known π / 4

∵ π / 4 ＜ α＜ 3 π / 4, ∵ π / 2 ＜ π / 4 + α＜ π, and COS (π / 4 + α) = - 3 / 5,
∴sin（π/4＋α）＝√［1－（－3/5）^2］＝4/5.
∵ 0 ＜ β＜ π / 4, ∵ 3 π / 4 ＜ 3 π / 4 + β＜ π, and sin (3 π / 4 + β) = 5 / 13,
∴cos（3π/4＋β）＝－√［1－（5/13）^2］＝－12/13.
∴sin（α＋β）＝－sin［π＋（α＋β）］＝－sin［（π/4＋α）＋（3π/4＋β）］
＝－sin（π/4＋α）cos（3π/4＋β）－cos（π/4＋α）sin（3π/4＋β）
＝－（4/5）（－12/13）－（－3/5）（5/13）＝（48＋15）/（5×13）＝63/（5×13）
＝63/65.

As shown in the figure, ⊙ o is the inscribed circle of equilateral △ ABC with side length 2, then the radius of ⊙ o is___ ．

Connect OC and tangent point D, as shown in the figure, the center of equilateral triangle is the center line, the bottom edge is high, and the intersection point of angle bisector is OD ⊥ BC, ∠ OCD = 30 °, OD is the radius of the circle. And by BC = 2, CD = 1. So in the right triangle OCD, odcd = tan30 ° is substituted into the solution: od = 33. So the answer is 33

Using discriminant method to find function range
Given the function y = x - (2 / x) + 2, find the function range
1. If discriminant method is used,
2. Is there any other solution to this problem,
Please don't skip 1 and answer 2,
But according to the image, y is not equal to 0. Why?

The discriminant method cannot be used. The premise of discriminant method is that the definition field of X is r, and the definition field of this problem is not all real numbers
And the first floor at the same time multiplied by X symbol is uncertain, can not carry on multiplication operation!
It is more troublesome to use the domain method
In fact, derivation is the easiest!
Because x is not equal to 0, X - (2 / x) is not equal to - 2, that is, y = x - (2 / x) + 2 is not equal to 0

What is the invariance of differential forms

When u is an independent variable, y = f (U), Dy = f '(U) Du
When u is an intermediate variable, y = f (U), u = g (x), y = f [g (x)], Dy = f '[g (x)] g' (x) DX = f '(U) Du
There is still dy = f ′ (U) Du
That is to say, whether u is an intermediate variable or an independent variable, y = f (U), then there is always a differential
dy=f′(u)du
This is the invariance of differential forms