Knowing 1 x 2 x 1 1 4, find the value of 1 x 4 x 2 1 .

Knowing that 1 (x +x+1) = 1 4 , find the value of 1 (x +x +1).

Solution: 1 (x +x+1)=1 4, x +x+1=4;x²+x=3；

x⁴+x²+1=(x²+x)²-2x³+1=9-2x³+1=10-2x³..1)；

and x -1 = (x-1) (x + x + 1) = 4 (x-1), so x = 4x-3 is substituted into (1) to obtain:

x⁴+x²+1=10-2(4x-3)=16-8x=8(2-x)..2)；

Then from x +x=3 we get x +x-3=0;Therefore x=(-1 13) 2;Substituting equation (2) to obtain:

x⁴+x²+1=8[2-(-1±√13)/2]=8[(5±√13)/2]=4(5±√13)

Therefore 1 (x +x +1)=1 [4(5 13)].

i.e. 1 (x +x +1) = 1 [4(5 + 13)] = (5- 13) [4(25-13)] = (5- 13) 48

or 1 (x +x +1) = 1 [4(5-13)] = (5 + 13) [4(25-13)] = (5 + 13) 48

Simplify from 1 (x 2+x+1)=1 4 to get x 2=3-x, using the formula x 2=3-x to reduce the order (x is reduced from 2 times to 1 time), this kind of problem is this way.

So x 4+x 2+1=(3-x) 2+x 2+1=2x 2-6x+10=2(3-x)-6x+10=-8x+16 becomes 1 time. Then solve x from x 2=3-x, and then substitute it into -8x+16.

First, divide each side of the equation to get :

x-2)-(x-1)

x-4)-(x-3)

The cut-off score ---

x-1)(x-2)

x-3)(x-4)

x-1)(x-2)

x-3)(x-4)

x-3)(x-4)

x-1)(x-2)

x^2-7x+12

x^2-3x+2-4x

X-test: X-1≠0, X-2≠0, X-3≠0, X-4≠0

x= is the solution of the original fractional equation.

Fight with all hands, beg the landlord! )

Solution: x -5x = 14

x-1)(2x-1)-(x+1)²+1

2x²-3x+1)-(x²+2x+1)+12x²-3x+1-x²-2x-1+1

x²-5x+1

15 That is, what is desired.

This question examines the multiplication of polynomials, as well as the addition and subtraction of integer expressions, and the evaluation of global substitution, and the parentheses are easy to disassemble.

Hopefully, I hope it will help you.

x^2-5x-14=0

x+2)(x-7)=0

x=-2 or x=7

So (x-1)(2x-1)-(x+1) 2+1x=-2 equals 15

x=7 equals 15

So (x-1)(2x-1)-(x+1) 2+1=15

Upstairs, while you're right, but you're having a problem with your algorithm, it should be.

x2+1 x2=(x+1 x) 2-2 is brought into (1) where (x+1 x)=4

Vested 16-2=14

First, let you ask for 1 x to mean that x is not zero.

Down, divide x2-4x+1=0 by x at the same time

1) The result is 4

2) With (x+1 x) 2=x2+1 x2+2, the result is 14

Upstairs,Is this obviously a mistake from him?。。。

(1) x -4x+1=0 yields: x +1=4x

x+1/x=（x²+1）/x=4x/x=4

2) What is the value of "=" in the middle?

Knowing x -5x=14, so x -5x-14=0, (x-7)(x+2)=0, gives x=7x=-2, when x=7, (x-1)(2x-1)-(x+1) +1=6 times 13-64+1=15, when x=-2, (x-1)(2x-1)-(x+1) +1=-3 multiplied by (-5)-1+1=15, so the value of (x-1)(2x-1)-(x+1) +1 is 15

Solution: x (x -x+1)=5

x²-x+1)/x=1/5

x-1+1/x=1/5

x+1/x=6/5

x+1/x)²=6/5)²

x²+1/x²=-14/25

x 4+x +1) x Chazao.

x²+1/x²+1

14 defeats with 25+1

x²/(x^4+x²+1)=25/11.

Note: Actually, the uncontested chiropractic x of this problem can only be solved in the range of complex numbers. ]