Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a)
\(A=\dfrac{2x^2-16x+41}{x^2-8x+22}=\dfrac{2\left(x^2-8x+22\right)-3}{x^2-8x+22}\)
\(A-2=-\dfrac{3}{x^2-8x+22}=-\dfrac{3}{\left(x-4\right)^2+6}\ge-\dfrac{3}{6}=-\dfrac{1}{2}\)
\(A\ge\dfrac{3}{2}\) khi x =4
a) M xác định \(\Leftrightarrow4x^3-9x\ne0\)
\(\Leftrightarrow x\left(4x^2-9\right)\ne0\\ \Leftrightarrow\left[{}\begin{matrix}x\ne0\\x\ne\pm\dfrac{3}{2}\end{matrix}\right.\)
b)
\(M=\dfrac{\left(2x^3+3x^2\right)\left(2x+1\right)}{4x^3-9x}=\dfrac{4x^4+2x^3+6x^3+3x^2}{4x^3-9x}\\ =\dfrac{4x^4+8x^3+3x^2}{4x^3-9x}\\ =\dfrac{x\left(4x^3+8x^2+3x\right)}{x\left(x^2-9\right)}\\ =\dfrac{4x^3+8x^2+3x}{x^2-9}\)
c)
\(M=0\\ \Leftrightarrow\left(2x^3+3x^2\right)\left(2x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x^3+3x^2=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2\left(2x+3\right)=0\\x=-\dfrac{1}{2}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{3}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
a: \(Q=\dfrac{x^2-4x+3+2x+6-x^2-3}{\left(x-3\right)\left(x+3\right)}:\dfrac{2x-1-2x-1}{2x+1}\)
\(=\dfrac{-2x+6}{\left(x-3\right)\left(x+3\right)}\cdot\dfrac{2x+1}{-2}\)
\(=\dfrac{2x+1}{x+3}\)
b: ta có: |x+1|=1/2
=>x+1=1/2 hoặc x+1=-1/2
=>x=-3/2
Thay x=-3/2 vào A, ta được:
\(A=\left(2\cdot\dfrac{-3}{2}+1\right):\left(\dfrac{-3}{2}+3\right)=-2:\dfrac{3}{2}=-\dfrac{4}{3}\)
c: Để Q=2 thì 2x+1=2x+6
=>\(x\in\varnothing\)
a) điều kiện xát định : \(x\ne\pm1\)
ta có : \(P=\left(\dfrac{x-2}{x^2-1}-\dfrac{x+2}{x^2+2x+1}\right).\left(\dfrac{1-x^2}{2}\right)^2\)
\(P=\left(\dfrac{x-2}{\left(x-1\right)\left(x+1\right)}-\dfrac{x+2}{\left(x+1\right)^2}\right).\dfrac{\left(1-x\right)^2\left(1+x\right)^2}{4}\)
\(P=\dfrac{x-2}{\left(x-1\right)\left(x+1\right)}.\dfrac{\left(x-1\right)^2\left(x+1\right)^2}{4}-\dfrac{x+2}{\left(x+1\right)^2}.\dfrac{\left(x-1\right)^2\left(x+1\right)^2}{4}\)
\(P=\dfrac{\left(x-2\right)\left(x-1\right)\left(x+1\right)}{4}-\dfrac{\left(x+2\right)\left(x-1\right)^2}{4}\)
\(P=\dfrac{\left(x-2\right)\left(x-1\right)\left(x+1\right)-\left(x+2\right)\left(x-1\right)^2}{4}\)
\(P=\dfrac{\left(x-1\right)\left(\left(x-2\right)\left(x+1\right)-\left(x+2\right)\left(x-1\right)\right)}{4}\)
\(P=\dfrac{\left(x-1\right)\left(x^2-x-2-\left(x^2+x-2\right)\right)}{4}\)
\(P=\dfrac{\left(x-1\right)\left(x^2-x-2-x^2-x+2\right)}{4}=\dfrac{\left(x-1\right)\left(-2x\right)}{4}\)
\(P=\dfrac{-2x^2+2x}{4}\)
b) ta có : \(P-4=5x\Leftrightarrow\dfrac{-2x^2+2x}{4}-4=5x\)
\(\Leftrightarrow\dfrac{-2x^2+2x-16}{4}=5x\Leftrightarrow-2x^2+2x-16=20x\)
\(\Leftrightarrow20x-\left(-2x^2+2x-16\right)=0\Leftrightarrow2x^2+18x+16=0\)
\(\Leftrightarrow2x^2+2x+16x+16=0\Leftrightarrow2x\left(x+1\right)+16\left(x+1\right)=0\)
\(\Leftrightarrow\left(2x+16\right)\left(x+1\right)\Leftrightarrow\left[{}\begin{matrix}2x+16=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-8\left(tmđk\right)\\x=-1\left(loại\right)\end{matrix}\right.\)
vậy \(x=-8\) thỏa mãng điều kiện bài toán
a, Rút gọn Biểu thức:
A=\(\left(\dfrac{x+2}{2x-4}-\dfrac{x-2}{2x+4}\right):\dfrac{2x}{x2+2x}\)
= \(\left(\dfrac{x+2}{2x-4}+\dfrac{-x-2}{2x+4}\right):\dfrac{2x}{x2+2x}\)
= \(\left(\dfrac{x+2+-x-2}{2x-4+2x+4}\right):\dfrac{2x}{x2+2x}\)
= 0 \(:\dfrac{2x}{x2+2x}\)
b, \(\left(\dfrac{x+2}{2x-4}-\dfrac{x-2}{2x+4}\right):\dfrac{2x}{x2+2x}\)
Thay tất cả x= -4
=> \(\left(\dfrac{-4+2}{2-4-4}-\dfrac{-4-2}{2-4+4}\right):\dfrac{2.-4}{-4.2+2.-4}\)
= -16 : \(\dfrac{1}{3}\)
= -18
\(b,Q=-5x^2-4x+1\)
\(=-5\left(x^2+\dfrac{4}{5}x+\dfrac{4}{25}\right)+\dfrac{9}{5}\)
\(=-5\left(x+\dfrac{2}{5}\right)^2+\dfrac{9}{5}\)
Với mọi giá trị của x ta có:
\(-5\left(x+\dfrac{2}{5}\right)^2\le0\)
\(\Rightarrow-5\left(x+\dfrac{2}{5}\right)^2+\dfrac{9}{5}\le\dfrac{9}{5}\)
Vậy MaxQ = \(\dfrac{9}{5}\)
Để Q = \(\dfrac{9}{5}\) thì \(x+\dfrac{2}{5}=0\Rightarrow x=-\dfrac{2}{5}\)
\(c,K=x\left(x-3\right)\left(x-4\right)\left(x-7\right)\)
\(=x\left(x-7\right)\left(x-3\right)\left(x-4\right)\)
\(=\left(x^2-7x\right)\left(x^2-7x+12\right)\)
Đặt \(x^2-7x+6=t\) , ta có:
\(K=\left(t-6\right)\left(t+6\right)\)
\(=t^2-36\)
\(=\left(x^2-7x+6\right)^2-36\)
Với mọi giá trị của x ta có:
\(\left(x^2-7x+6\right)^2\ge0\Rightarrow\left(x^2-7x+6\right)^2-36\ge-36\)
Vậy Min K = -36
Để K = - 36 thì \(x^2-7x+6=0\)
\(\Leftrightarrow x^2-x-6x+6=0\)
\(\Leftrightarrow x\left(x-1\right)-6\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-6\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-6=0\\x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=6\\x=1\end{matrix}\right.\)
a)\(P=2x^2-8x+1\)
=\(2\left(x^2-4x+4\right)-7\)
=\(2\left(x-2\right)^2-7\)
Với mọi x thì \(2\left(x-2\right)^2>=0\)
=>\(2\left(x-2\right)^2-7>=-7\)
Hay \(P>=-7\) với mọi x
Để \(P=-7\) thì
\(\left(x-2\right)^2=0\)
=>\(x-2=0\)
=>\(x=2\)
Vậy...
Các câu sau tương tự
\(\dfrac{2x^2+4x}{x^3-4x}+\dfrac{x^2-4}{x^2+2x}+\dfrac{2}{2-x}\)
\(=\dfrac{2x^2+4x}{x\left(x-2\right)\left(x+2\right)}+\dfrac{x^2-4}{x\left(x+2\right)}-\dfrac{2}{x-2}\)\(=\dfrac{2x^2+4x+\left(x^2-4\right)\left(x-2\right)-2x\left(x+2\right)}{x\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{2x^2+4x+x^3-2x^2-4x+8-2x^2-4x}{x\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^3-2x^2-4x+8}{x\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{\left(x^3+8\right)-\left(2x^2+4x\right)}{x\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{\left(x+2\right)\left(x^2-2x+4\right)-2x\left(x+2\right)}{x\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{\left(x+2\right)\left(x^2-2x+4-2x\right)}{x\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{\left(x+2\right)\left(x^2-4x+4\right)}{x\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{\left(x+2\right)\left(x-2\right)^2}{x\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x-2}{x}.\)