Knowing X X2 X 1 a, find X2 X4 X2 1 . Note X2 is X square, and X4 is X 4th power. Thank you very mu

Answer: A (1-2a).

It's a very simple question, actually.

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x / (x2+x+1) =a

The left side is divided by xx+1 x=1 a-1

Square on both sides. x2+1/x2=1/a2-2/a-1x2/（x4+x2+1）

1/(x2+1/x2+1)

a2/(2a2-2a+1)

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Solving equations with brute force? No, it doesn't.

x/(x²-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)

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x/x²-x+1=7

1-x²+x=7x

x² +6x -1=0

x = -3 ± 10

x² = 19±6√10

x²/x)^4+x²+1

x²)²x²+1

19 6 10) 19 6 10+1=(19 6 10) 18 6 10) and then you can calculate it yourself.

Because x (x -x+1) = 7, x-1+1 x = 1 7, x+1 x=8 7, (x+1 x) = 64 49, x +1 x +2 = 64 49, x +1 x +1 = 15 49

Let a=x (x to the fourth power + x to the square + 1).

then 1 a = x +1 + 1 x = 15 49

So a=49 15

x/x²-x+1=7

x²-x+1)/x=1/7

x+1/x-1=7

x+1/x=8

x to the fourth power + x to the square + 1 ) x

x²+1/x²+1

x+1/x)²-2+1

63x x to the fourth power + x squared + 1 = 1 63

x/x²-x+1=7

x/x²-x=6

Square on both sides. x x to the fourth power + x squared - 2 = 6

x x to the fourth power + x squared = 8

x/x²-x+1=a

Take the reciprocal x-1+1 x=1 a

x+1/x=1/a+1=(a+1)/a

x²+2+1/x²=（a+1）²/a²

And (x to the fourth power + x to the square + 1) x

x²+1/x²+1

a+1）²/a²-1

2a+1）/a²

So the original formula = a (2a+1).

x=ax²-ax+a

ax²+a=(a+1)x

Square on both sides. a x 4+2a x +a = (a +2a+1)x minus a x on both sides

a x 4+a x +a = (2a+1) x a (x 4+x +1) = (2a+1)x so x (x 4+x +1) = a (2a+1).

The equation is x2+1=5x, obviously x is not 0, the two ends are divided by x to get x+1 x=5, and the square is x 2+2+1 x 2=25, so x 2+1 x 2=23, and then squared to get x 4+2+1 x 4=529, so x 4+1 x 4=527. (The visual question seems to be incorrect.) If you find x 2+1 x 2, the result is 23.

If you find x 4+1 x 4, the result is 527. If you find (x 4+1) x 2, the result is x 2+1 x 2=23. But the result of x 4+1 x 2 is not very neat).

x²-5x+1=0

x²+1=5x

x+1/x=5

x +1 x = (x+1 x) 2-2 = 25-2 = 23x to the fourth power + 1 x to the fourth power.

x²+1/x²)^2-2=529-2=527

∵x²+x=1

x²+x-1=0

According to the root finding formula.

x⁴+x³-x²-2x+2005

x²(x²+x)-x²-2x+2005

x²×1-x²×-2x+2005

2005-2x

or 2006+5

I'm afraid that I will change the title and do it.

x⁴+2x³-x²-2x+2005

x⁴+x³+x³+x²-2x²-2x+2005=x²(x²+x)+x(x²+x)-2(x²+x)+2005=x²+x-2+2005

Did you make a mistake? The original formula = x 2-x 2-2x + 2005 = 2005-2x, and then you can calculate it by solving the original equation yourself.