Knowing x 2x 1, find the value of x 1 3x 1 x 1

x-1）（3x+1）- x＋1﹚²=3x²-2x-1-（x²+2x+1）

According to the first formula, 2x+1=x

So (x-1)(3x+1)- x 1 =3x -2x-1-(x +2x+1)=3x -x -x -2x-1=x -2x-1=0

x－1﹚﹙3x＋1﹚－﹙x＋1﹚²=2x²-4x-2=2(x²－2x)-2=2-2=0

Put the latter formula on it.

For 0, if you put the latter formula, you will get 2 (x2-2x-1), and the thing in parentheses is zero.

x+1 x=5 both sides squared at the same time to get x +2+1 x =25

x²+1/x²=25-2

x²+1/x²=23

I have a new question and ask for help, thank you!

This question is the application of the perfect square formula, and the calculation steps for the two questions are as follows:

1) When x+1 x=5, then:

x^2+1/x^2

x^2+2+1/x^2-2

x+1/x)^2-2

2) When x 2-1 x 2=5, then:

x^2-1/x^2)^2=25

x^4-2+1/x^4=25

x^4+1/x^4=27

x^4+2+1/x^4=29

x 2+1 x 2) 2=29, because it is the sum of squares, so:

x^2+1/x^2=√29.

The calculation of the two questions** is shown in the figure below:

Write on ** below.

Solution: Square the two sides of known x+1 x 5.

x²+1/x²+2＝25， x²+1/x²＝23.

Solution: Square the two sides of known x+1 x 5.

x +1 x -2 25, x +1 x +2 29, i.e. (x +1 x ) 29, x +1 x 0, x +1 x 29

x²-4x+1=0

Obviously, x≠0 is divided by x.

x-4+1/x=0

x+1/x=4

Both sides are squared.

x²+2+1/x²=16

x²+1/x²=14

Both sides are divided by x:

x² -4x + 1)/x=0/x

x - 4 + 1/x=0

x + 1/x=4

Squared on both sides: (x + 1 x).

x² +2 + 1/x²=16

then x +1 x = 14

The value is 2, the question is written incorrectly, you can take a look.

Both sides are divided by x:

x - 2 - 1/x=0

x - 1/x=√2

Square both sides: x -2 x (1 x) +1 x =2x -2 + 1 x =2

x² +1/x²=4

x 2-1 = root number 2 x

Divide by xx-1 x = root number 2 on both sides

Square on both sides. x^2+(1/x)^2-2=2

So the original formula = 2 + 2 = 4

Knowing that x (x -x+1) = 7, find the value of x (x x +x +1).

Solution: x (x -x+1) = 7

x²-x+1)/x=1/7

x-1+1/x=1/7

x+1/x=8/7

Square both sides: x +2 + 1 x = (8 7) x +1 x =(8 7) -2

x²/(x⁴+x ²+1)

1/((x⁴+x ²+1)/x²)

1/(x²+1+1/x²)