GHÉP THÀNH 2 ĐA THỨC BẬC HAI 

(X^4 + 2*X^3/2+x^2/4)+(X^2/4+2*X/2+1)+X^2/2

(X^2+x/2)^2+(X/2+1)^2+X^2/2

ĐÚNG THÌ K 

- Ta có: \(x^4+x^3+x^2+x+1=0\)( * )

- Nhân \(x-1\)vào cả hai vế của phương trình ( * ), ta có: 

             \(\left(x^4+x^3+x^2+x+1\right).\left(x-1\right)=0.\left(x-1\right)\)

        \(\Leftrightarrow x^5+x^4+x^3+x^2+x-x^4-x^3-x^2-x-1=0.\left(x-1\right)\)

        \(\Leftrightarrow x^5+\left(x^4-x^4\right)+\left(x^3-x^3\right)+\left(x^2-x^2\right)+\left(x-x\right)-1=0.\left(x-1\right)\)

        \(\Leftrightarrow\frac{x^5-1}{x-1}=0\)( ** )

        \(\Leftrightarrow x^5-1=0\)

        \(\Leftrightarrow x^5=1\)

        \(\Leftrightarrow x=1\)

- Thay \(x=1\)vào phương trình ( ** ), ta có: 

               \(\frac{1^5-1}{1-1}=\frac{1-1}{0}\)( vô nghiệm )

Vậy phương trình \(x^4+x^3+x^2+x+1=0\)vô nghiệm ( ĐPCM )

Hãy tham khảo ở đây

https://h.vn/hoi-dap/tim-kiem?q=Ng%C6%B0%E1%BB%9Di+ta+d%C3%B9ng+h%E1%BB%87+th%E1%BB%91ng+r%C3%B2ng+r%E1%BB%8Dc+%28g%E1%BB%93m+1+r%C3%B2ng+r%E1%BB%8Dc+%C4%91%E1%BB%99ng+v%C3%A0+1+r%C3%B2ng+r%E1%BB%8Dc+c%E1%BB%91+%C4%91%E1%BB%8Bnh%29+%C4%91%E1%BB%83+k%C3%A9o+m%E1%BB%99t+b%E1%BB%A9c+t%C6%B0%E1%BB%A3ng+c%E1%BB%95+b%E1%BA%B1ng+%C4%91%E1%BB%93ng+%28b%E1%BB%A9c+t%C6%B0%E1%BB%A3ng+%C4%91%E1%BA%B7c+ho%C3%A0n+to%C3%A0n%29+c%C3%B3+tr%E1%BB%8Dng+l%C6%B0%E1%BB%A3ng+P+%3D+5340N+t%E1%BB%AB+%C4%91%C3%A1y+h%E1%BB%93+s%C3%A2u+H+%3D+10m+l%C3%AAn.++H%C3%A3y+t%C3%ADnh%3A++a%29+L%E1%BB%B1c+k%C3%A9o+khi+b%E1%BB%A9c+t%C6%B0%E1%BB%A3ng+ch%C3%ACm+ho%C3%A0n+to%C3%A0n+d%C6%B0%E1%BB%9Bi+n%C6%B0%E1%BB%9Bc.++b%29+T%C3%ADnh+c%C3%B4ng+c%E1%BA%A7n+thi%E1%BA%BFt+%C4%91%E1%BB%83+k%C3%A9o+b%E1%BB%A9c+t%C6%B0%E1%BB%A3ng+t%E1%BB%AB+%C4%91%C3%A1y+h%E1%BB%93+l%C3%AAn+%C4%91%E1%BA%BFn+m%E1%BA%B7t+n%C6%B0%E1%BB%9Bc.+B%E1%BB%8F+qua+tr%E1%BB%8Dng+l%C6%B0%E1%BB%A3ng+c%E1%BB%A7a+c%C3%A1c+r%C3%B2ng+r%E1%BB%8Dc.+Bi%E1%BA%BFt+tr%E1%BB%8Dng+l%C6%B0%E1%BB%A3ng+ri%C3%AAng+c%E1%BB%A7a+%C4%91%E1%BB%93ng+l%C3%A0+89000N%2Fm3&subject=0

nhớ cho mình k nếu đúng nhé

Bài làm

x( 2x - 9 ) = 3x( x - 5 )

<=> 2x² - 9x = 3x² - 15x 

<=> 2x² - 3x² = 9x - 15x

<=> -x² = -6x

<=> x² + 6x = 0

<=> x( x + 6 ) = 0

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

Vậy tập nghiệm S = { 0; -6 }

# Học tốt #

2x^2 -9x=3x^2 -15x

2x^2 -9x-3x^2 +15x=0

-x^2 +4x=0

-x(x-4)=0

x-4=0

x=4

9+9=18

X thuộc Z

\(x-2120=\frac{3}{4}\left(21210-x+2121\right)\)

\(x-2120=-\frac{3x}{4}+\frac{69993}{4}\)

\(x=\frac{-3x+69993}{4}+2120\)

\(x\cdot \:4=\frac{-3x+69993}{4}\cdot \:4+2120\cdot \:4\)

\(4x=-3x+69993+8480\)

\(4x=-3x+78473\)

\(4x+3x=-3x+78473+3x\)

\(7x=78473\)

\(x=78473:7\)

\(x=\frac{78473}{7}\)

\(\frac{3}{x^2-1}\left(x\ne\pm1\right)\)

Phân số đạt được GTLN khi x²-1 đạt GTNN

=> x²-1=1

=> x²=2

=> \(x=\pm\sqrt{2}\left(tm\right)\)