\(x^4-30x^2+31x-30=0\)

\(\left(x^4+x\right)-30\left(x^2-x+1\right)=0\)

\(x\left(x^3+1\right)-30\left(x^2-x+1\right)=0\)

\(x\left(x+1\right)\left(x^2-x+1\right)-30\left(x^2-x+1\right)=0\)

\(\left(x^2-x+1\right)\left[x\left(x+1\right)-30\right]=0\)

Ta có: \(x^2-x+1=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}>0\)

\(\Rightarrow x^2+x-30=0\left(x^2-x+1\ne0\right)\)

\(\left(x^2-5x\right)+\left(6x-30\right)=0\)

\(x\left(x-5\right)+6\left(x-5\right)=0\)

\(\left(x-5\right)\left(x+6\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-5=0\\x+6=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=5\\x=-6\end{cases}}}\)

Vậy \(\orbr{\begin{cases}x=5\\x=-6\end{cases}}\)

Thanks bạn nha

             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

x^4 - 30x^2 + 31x - 30 = 0
<=> x^4 + x^3 - 30x^2 - x^3 - x^2 + 30x+ x^2 + x - 30 = 0
<=> x^2(x^2 + x - 30) - x(x^2 + x - 30) + (x^2 + x - 30) = 0
<=> (x^2 - x + 1)(x^2 + x - 30) = 0
<=> (x^2 - x + 1)(x + 6)(x - 5) = 0
Mà x^2 - x + 1 = (x^2 - 2.x.1/2 + 1/4) + 3/4 = (x - 1/2)^2 + 3/4 > 0
=> x = -6 hoặc x = 5

hc tốt ~:B~

x^4 - 30x^2 + 31x - 30 = 0
<=> x^4 + x^3 - 30x^2 - x^3 - x^2 + 30x+ x^2 + x - 30 = 0
<=> x^2(x^2 + x - 30) - x(x^2 + x - 30) + (x^2 + x - 30) = 0
<=> (x^2 - x + 1)(x^2 + x - 30) = 0
<=> (x^2 - x + 1)(x + 6)(x - 5) = 0
Mà x^2 - x + 1 = (x^2 - 2.x.1/2 + 1/4) + 3/4 = (x - 1/2)^2 + 3/4 > 0
=> x = -6 hoặc x = 5

\(x^4-30x^2+31x-30=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+6\right)\left(x^2-x+1\right)=0\)

Vì: \(x^2-x+1=x^2-2x.\frac{1}{2}+\frac{1}{4}+\frac{3}{4}=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}>0\forall x\)

\(\Leftrightarrow\orbr{\begin{cases}x+5=0\\x-6=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=5\\x=-6\end{cases}}\)

Vậy: x = 5 hoặc x = -6

Đề là gì vậy bn ????

\(x^4-30x^2+31x-30=0\)

\(\Leftrightarrow x^4+x-30x^2+30x-30=0\)

\(\Leftrightarrow x\left(x^3+1\right)-30\left(x^2-x+1\right)=0\)

\(\Leftrightarrow x\left(x+1\right)\left(x^2-x+1\right)-30\left(x^2-x+1\right)=0\)

\(\Leftrightarrow\left(x^2-x+1\right)\left(x^2+x-30\right)=0\)

\(\Leftrightarrow\left(x^2-x+1\right)\left(x+6\right)\left(x-5\right)=0\)

Ta có: \(x^2-x+1=x^2-2.x.\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{3}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge0\forall x\in R\)

\(\Rightarrow\left(x-5\right)\left(x+6\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-6\end{matrix}\right.\)

Vậy, \(S=\left\{-6;5\right\}\)

x^4-30x^2+31x^2-30=0

=>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+1)(x^2-5x+6x-30)=0

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

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

vì x^2-x+1=x^2-2x.(1/2)+1/4+3/4

=(x-1/2)^2+3/4>0 với mọi x

Do đó x-5=0 hoac x+6=0

=>x=5 hoặc x=-6

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

\(x^4-30x^2+31x-30=0\)

\(\Leftrightarrow x^4+x-30x^2+30x-30=0\)

\(\Leftrightarrow\left(x^4+x\right)-\left(30x^2-30x+30\right)=0\)

\(\Leftrightarrow x\left(x^3+1\right)-30\left(x^2-x+1\right)=0\)

\(\Leftrightarrow x\left(x+1\right)\left(x^2-x+1\right)-30\left(x^2-x+1\right)=0\)

\(\Leftrightarrow\left(x^2-x+1\right)\left[x\left(x+1\right)-30\right]=0\)

\(\Leftrightarrow\left(x^2-x+1\right)\left(x^2+x-30\right)=0\)

\(\Leftrightarrow\left(x^2-x+1\right)\left(x^2-5x+6x-30\right)=0\)

\(\Leftrightarrow\left(x^2-x+1\right)\left[\left(x^2-5x\right)+\left(6x-30\right)\right]=0\)

\(\Leftrightarrow\left(x^2-x+1\right)\left[x\left(x-5\right)+6\left(x-5\right)\right]=0\)

\(\Leftrightarrow\left(x^2-x+1\right)\left(x-5\right)\left(x+6\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2-x+1=0\\x-5=0\\x+6=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}>0\left(loai\right)\\x=5\\x=-6\end{matrix}\right.\)

Vậy x=5 hoặc x=-6