Rút gọn biểu thức:
\(2\mid x-3 \mid - \mid 4x -1 \mid\)
Tìm GTNN
a. \(\mid x-7\mid\) + \(\mid x+5\mid\)
b. \((2x-1)^2 -3\mid2x-1\mid +2\)
c.\(\mid x^2 + x + 1\mid + \mid x^2 +x -12\mid\)
a) Bạn adct \(\left|x\right|+\left|y\right|\ge\left|x+y\right|\)
Ta cóA= \(\left|x-7\right|+\left|x+5\right|=\left|7-x\right|+\left|x+5\right|\ge\left|7-x+x+5\right|\)
=> \(\left|7-x\right|+\left|x+5\right|\ge12\) vậy minA=12
b)Ta có \(\left(2x-1\right)^2-3\left|2x-1\right|+2=\left|2x-1\right|^2-2\left|2x-1\right|.\frac{3}{2}+\frac{9}{4}-\frac{1}{4}=\left(\left|2x-1\right|-\frac{3}{2}\right)^2-\frac{1}{4}\)=>minA=-1/4
còn câu c thì bạn làm giống câu a nhé
Giải phương trình: \(\mid x^2 -2xy+y^2 +3x-2y-1 \mid+4=2x-\mid x^2 -3x+2 \mid\)
Tìm GTNN của các biểu thức:
\(A= \mid x-1 \mid + \mid x-2017 \mid\)
\(B=(x-5)^2+\mid x-5\mid+2014\)
Giúp mình nha!!!!!!!!!!!!!!!!!!!!!!!!!
a, Ta có: \(A=\left|x-1\right|+\left|x-2017\right|=\left|x-1\right|+\left|2017-x\right|\)
Áp dụng bất đẳng thức \(\left|a\right|+\left|b\right|\ge\left|a+b\right|\) ta có:
\(A\ge\left|x-1+2017-x\right|=\left|-2016\right|=2016\)
Dấu " = " khi \(\left\{{}\begin{matrix}x-1\ge0\\2017-x\ge0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ge1\\x\le2017\end{matrix}\right.\Rightarrow1\le x\le2017\)
Vậy \(MIN_A=2016\) khi \(1\le x\le2017\)
b, Ta có: \(\left\{{}\begin{matrix}\left(x-5\right)^2\ge0\\\left|x-5\right|\ge0\end{matrix}\right.\Rightarrow\left(x-5\right)^2+\left|x-5\right|\ge0\)
\(\Rightarrow B=\left(x-5\right)^2+\left|x-5\right|+2014\ge2014\)
Dấu " = " khi \(\left\{{}\begin{matrix}\left(x-5\right)^2=0\\\left|x-5\right|=0\end{matrix}\right.\Rightarrow x=5\)
Vậy \(MIN_B=2014\) khi x = 5
Giải phương trình: \(\mid\)x2 -2xy+y2 +3x- 2y-1\(\mid\) +4= 2x-\(\mid\) x2 -3x+2\(\mid\).
B/ Mid – Autumn Festival
There are hundreds of festival in Vietnam each year. (1)………., Tet holiday, the Mid- Autumn festival is one of the most famous festival and it is a traditional celebration for Vietnamese (2)…………
The Mid – Autumn Festival is (3)………….. on the 15th day on the 8th lunar month ( often in late Semtember or early October) in the middle of Autumn and it is celebrated for a whole day. On this day , the adults and the parents prepare a special cake called moon cake along with many candies, jellies, grapefruit, bananas, apples, etc. Tha Mid- autumn celebration is an opportunity (4) …………………. Family members to reunite. Young people express their gratitude to the elderly.
Question 1: A. and B. therefore C. besides D. so
Question 2: A. children B. child C. girls D. boys
Question 3: A. held B. remembered C. taken D. done
Question 4: A. on B. for C. in D. at
tìm giá trị nhỏ nhất của biểu thức:
A=
x+5 + 3-xCó: \(\left|x+5\right|\ge x+5;\left|3-x\right|\ge3-x\forall x\)
\(\Rightarrow A=\left|x+5\right|+\left|3-x\right|\ge x+5+3-x=8\)
Dấu ''='' xảy ra khi \(\begin{cases}x+5\ge0\\3-x\ge0\end{cases}\)\(\Rightarrow\begin{cases}x\ge-5\\x\le3\end{cases}\)
Vậy GTNN của A là 8 khi \(-5\le x\le3\)
Cho Q = \(\frac{12x-45}{x^2-7x+12}-\frac{x+5}{x-4}+\frac{2x-3}{3-x}\)
a) Rút gọn Q b)Tính giá trị của Q tại \(\mid\)x\(\mid\) = 3
c) Tìm x \(\in\)Z để Q nhận giá trị nguyên
a) Rút gọn :
ĐKXĐ : \(x\ne4,x\ne3\)
Ta có : \(Q=\frac{12x-45}{x^2-7x+12}-\frac{x+5}{x-4}+\frac{2x-3}{3-x}\)
\(=\frac{3\left(4x-15\right)}{\left(x-4\right)\left(x-3\right)}-\frac{\left(x+5\right)\left(x-3\right)}{\left(x-4\right)\left(x-3\right)}-\frac{\left(2x-3\right)\left(x-4\right)}{\left(x-4\right)\left(x-3\right)}\)
\(=\frac{12x-45-x^2-2x+15-2x^2+11x-12}{\left(x-4\right)\left(x-3\right)}\)
\(=\frac{-3x^2+21x-42}{\left(x-4\right)\left(x-3\right)}\)
... Chắc tui rút gọn sai òi :))
\(\mid\)\(\mid\)3x-3\(\mid\)+2x+\(\left(-1\right)^{2006}\)=3x+\(2017^0\)
Rút gọn
a) A= \(\sqrt{3+\sqrt{5}}\) - \(\sqrt{3-\sqrt{5}}\)
b) B= 2\(\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}\)