x3 +2x - 3 = 0
HELP ME!!!
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
em moi hoc lop 5 thoi nen thong cam nhe tri nhan bao
Ta có:
x1 + x2 + x3 + ... + x2008 + x2009 + x2010
= (x1 + x2 + x3) + ... + (x2008 + x2009 + x2010)
= 1 + 1 + 1 + ... + 1(670 số 1)
= 670
\(\Rightarrow\) x1 + x2 + x3 + ... + x2009 + x2010 + x2011 = 670 + x2011 = 0
\(\Rightarrow\) x2011 = -670
M = x3 + x2y - 2x2 - xy - y2 + 3y + x + 2017
M = (x3 + x2y - 2x2) - (xy + y2 - 2y) + (x + y - 2) + 2019
M = x2. (x + y - 2) - y(x + y - 2) + (x + y - 2) + 2019 = 2019
\(M = x^3 + x^2y - 2x^2 - xy - y^2 + 3y + x + 2017.\)
\(M=(x^3+x^2y-2x^2)-(xy-y^2+2y)+(x+y-2)+2019\)
\(M=x^2.(x+y-2)-y.(x-y+2)+(x+y-2)+2019\)
\(M=x^2.0-y.0+0+2019\)
\(M=0-0+0+2019\)
\(M=2019\)
vì \(x^4+2x^2+1=\left(x^2+1\right)^2\) mà \(x^2\ge0\Rightarrow x^2+1>0\Rightarrow\left(x^2+1\right)^2>0\)với mọi x.Nên x-3=0 .Từ đó suy ra x=3
(2x-3)(x+\(\frac{1}{4}\))=0
\(\Leftrightarrow\orbr{\begin{cases}2x-3=0\\x+\frac{1}{4}=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{3}{2}\\x=\frac{-1}{4}\end{cases}}}\)
Bài làm
Ta có: \(\left(2x-3\right)\left(x+\frac{1}{4}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x-3=0\\x+\frac{1}{4}=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{3}{2}\\x=-\frac{1}{4}\end{cases}}}\)
Vậy x = 3/2 hoặc x = -1/4
(2x+1)+(3-x)=0
=>2x+1=-3+x
=>2x+1-x=-3
=>x+1=-3
=>x=-3-1=-4
Vậy x=-4
\(x^3+2x-3=0\)
\(\Leftrightarrow\left(x^3-x^2\right)+\left(x^2-x\right)+\left(3x-3\right)=0\)
\(\Leftrightarrow x^2\left(x-1\right)+x\left(x-1\right)+3\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2+x+3\right)=0\)
Ta có: \(x^2+x+3=\left[x^2+2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\right]+3-\left(\dfrac{1}{2}\right)^2\)
\(=\left(x+\dfrac{1}{2}\right)^2+\dfrac{11}{4}\)
Vì \(\left(x+\dfrac{1}{2}\right)^2\ge0\forall x\Rightarrow\left(x+\dfrac{1}{2}\right)^2+\dfrac{11}{4}\ge\dfrac{11}{4}>0\forall x\) (1)
Mà \(\left(x-1\right)\left(x^2+x+3\right)=0\) từ (1) \(\Rightarrow x-1=0\Leftrightarrow x=1\)
Vậy x = 1
\(x^3-x+3x-3=0\)
\(\Leftrightarrow x\left(x^2-1\right)+3\left(x-1\right)=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x+1\right)+3\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[x\left(x+1\right)+3\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2+x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x^2+x+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x^2+2x.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{4}+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\\left(x+\dfrac{1}{2}\right)^2+\dfrac{11}{4}=0\left(vl\right)\end{matrix}\right.\)
vậy \(S=\left\{1\right\}\)