x⁴-30x²+31x-30 =0

<=>  x⁴- x - 30x²+30x - 30 =0

<=> x ( x³- 1) - 30 (x² - x + 1)  =0

<=> x ( x-1) ( x² - x + 1) - 30 (x² - x + 1)  =0

<=>(x ( x-1) - 30) ( x² - x + 1) =0

<=>(x² -x -30) ( x² - x + 1) =0

<=>( x² - x + 1) ( x² - 5x + 6x - 30) =0

<=> ( x² - x + 1) ( x(x-5) + 6 ( x-5)) =0

<=> ( x² - x + 1) (x-5) (x+6) =0

Vì ( x² - x + 1) > 0 với mọi x (bình phương thiếu)

=> (x-5) (x+6) =0

<=> x-5 = 0 hoặc x+ 6 = 0

<=> x=5 hoặc x = -6

30x2=60

Đề là gì vậy bn ????

a: Ta có: x=31

nên x-1=30

Ta có: \(A=x^3-30x^2-31x+1\)

\(=x^3-x^2\left(x-1\right)-x^2+1\)

\(=x^3-x^3+x^2-x^2+1\)

=1

c: Ta có: x=16

nên x+1=17

Ta có: \(C=x^4-17x^3+17x^2-17x+20\)

\(=x^4-x^3\left(x+1\right)+x^2\left(x+1\right)-x\left(x+1\right)+20\)

\(=x^4-x^4-x^3+x^3+x^2-x^2-x+20\)

\(=20-x=4\)

d: Ta có: x=12

nên x+1=13

Ta có: \(D=x^{10}-13x^9+13x^8-13x^7+...+13x^2-13x+10\)

\(=x^{10}-x^9\left(x+1\right)+x^8\left(x+1\right)-x^7\left(x+1\right)+...+x^2\left(x+1\right)-x\left(x+1\right)+10\)

\(=10-x\)

=-2

d: Ta có: x=12

nên x+1=13

Ta có: \(D=x^{10}-13x^9+13x^8-13x^7+...+13x^2-13x+10\)

\(=x^{10}-x^9\left(x+1\right)+x^8\left(x+1\right)-x^7\left(x+1\right)+...+x^2\left(x+1\right)-x\left(x+1\right)+10\)

\(=x^{10}-x^{10}-x^9+x^9+x^8-x^8-x^7+...+x^3+x^2-x^2-x+1+9\)

\(=-x+10=-2\)

bạn gì ơi bạn làm thế thì chết giở mình rồi 

mình tưởng phải rút gọn chứ xong mới tính chứ 

làm thế ai chả làm được

x^4-5x^3+5x^3-25x^2-5x^2+25x+6x-30=0

(x-5)(x^3+5x^2-5x+6)=0

(x-5)(x^3+6x^2-x^2-6x+x+6)=0

(x-5)(x+6)(x^2-x+1)=0

Suy ra x-5=0 hay x+6=0 hay x^2-x+1=0

Suy ra x=5 hay x=-6 hay x^2+2x.1/2+1/4+3/4=0

Suy ra x=5 hay x=-6 hay (x+1/2)^2=3/4=0 (vô lý)

Vậy x=5 hay x=-6

\(x^4-30x^2+31x-30\)

\(=x^4+x-30x^2+30x-30\)

\(=x\left(x^3+1\right)-30\left(x^2-x+1\right)\)

\(=x\left(x+1\right)\left(x^2-x+1\right)-30\left(x^2-x+1\right)\)

\(=\left(x^2+x\right)\left(x^2-x+1\right)-30\left(x^2-x+1\right)\)

\(=\left(x^2-x+1\right)\left(x^2+x-30\right)\)

\(x^4-30x^2+31x-30\)

\(=x^4-5x^3+5x^3-25x^2-5x^2+25x+6x-30\)

\(=x^3\left(x-5\right)+5x^2\left(x-5\right)-5x\left(x-5\right)+6\left(x-5\right)\)

\(=\left(x-5\right)\left(x^3+5x^2-5x+6\right)\)

\(=\left(x-5\right)\left(x^3+6x^2-x^2-6x+x+6\right)\)

\(=\left(x-5\right)\left[x^2\left(x+6\right)-x\left(x+6\right)+\left(x+6\right)\right]\)

\(=\left(x-5\right)\left(x+6\right)\left(x^2-x+1\right)\)

x4−30x2+31x−30

=x4+x−30x2+30x−30

=x(x3+1)−30(x2−x+1)

=x(x+1)(x2−x+1)−30(x2−x+1)

=(x2+x)(x2−x+1)−30(x2−x+1)

=(x2−x+1)(x2+x−30)

pt <=> (x^4+x)-(30x^2-30x+30) = 0

<=> x.(x^3+1)-30.(x^2-x+1) = 0

<=> x.(x+1).(x^2-x+1)-30.(x^2-x+1) = 0

<=> (x^2-x+1).(x^2+x-30) = 0

<=> x^2+x-30 = 0 ( vì x^2-x+1 > 0 )

<=> (x^2-5x)+(6x-30) = 0

<=> (x-5).(x+6) = 0

<=> x-5=0 hoặc x+6=0

<=> x=5 hoặc x=-6

Vậy ..............

Tk mk nha