1. So sánh
a, (x-1)-(x+3)
b, (x+1)2=25
c, (x-1).(5-x)>0
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16 tháng 12 2023
b: \(\left(2x+1\right)^2=25\)
=>\(\left[{}\begin{matrix}2x+1=5\\2x+1=-5\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}2x=4\\2x=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)
c: \(\left(1-3x\right)^3=64\)
=>\(\left(1-3x\right)^3=4^3\)
=>1-3x=4
=>3x=1-4=-3
=>x=-3/3=-1
d: \(\left(4-x\right)^3=-27\)
=>\(\left(4-x\right)^3=\left(-3\right)^3\)
=>4-x=-3
=>x=4+3=7
e: \(x^2-5x=0\)
=>\(x\left(x-5\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\)
14 tháng 6 2020
Ta có:
A=\(x\cdot\left(-2016\right)\cdot\left(-2017\right)\cdot\left(-2018\right)\cdot\left(-2019\right)\)
Vì \(\left(-2016\right)\cdot\left(-2017\right)\cdot\left(-2018\right)\cdot\left(-2019\right)>0\)
\(\Rightarrow\)A\(\ge0\forall x\inℤ\)
B=\(x\cdot\left(-\left|-4\right|\right)\cdot\left(-1^2\right)\cdot\left(-3\right)^2\cdot\left(-2\right)^3-\left(-5\right)\)
\(=x\cdot\left(-4\right)\cdot9\cdot\left(-8\right)+5\)
\(=x\cdot\left(-36\right)\cdot\left(-8\right)+5\)
\(=x\cdot288+5>0\forall x\inℤ\)
Vậy A\(\ge0\forall x\inℤ\), B\(>0\forall x\inℤ\).
14 tháng 10 2021
\(1,\\ a,\Leftrightarrow4^{5-x}=4^2\Leftrightarrow5-x=2\Leftrightarrow x=3\\ b,\Leftrightarrow\left[{}\begin{matrix}x-1=5\\x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-4\end{matrix}\right.\\ c,\Leftrightarrow2x+1=3\Leftrightarrow x=2\\ 2,\\ a,3^{100}=\left(3^2\right)^{50}=9^{50}\\ b,2^{98}=\left(2^2\right)^{49}=4^{49}< 9^{49}\\ c,5^{30}=5^{29}\cdot5< 6\cdot5^{29}\\ d,3^{30}=\left(3^3\right)^{10}=27^{10}>8^{10}\\ 4,\\ a,\Leftrightarrow5\left(x-10\right)=10\\ \Leftrightarrow x-10=2\Leftrightarrow x=12\\ b,\Leftrightarrow3\left(70-x\right)+5=92\\ \Leftrightarrow3\left(70-x\right)=87\\ \Leftrightarrow70-x=29\\ \Leftrightarrow x=41\\ c,\Leftrightarrow16+x-5=315-230=85\\ \Leftrightarrow x=74\\ d,\Leftrightarrow2^x-5+74=707:\left(16-9\right)=707:7=101\\ \Leftrightarrow2^x=32=2^5\\ \Leftrightarrow x=5\)
11 tháng 3 2022
a: =>x=-7/6+5/8=-13/24
b: =>x=-14/25-3/4=-131/100
c: \(x=\dfrac{-33}{26}:\dfrac{-9}{13}=\dfrac{33}{26}\cdot\dfrac{13}{9}=\dfrac{11}{3}\cdot\dfrac{1}{2}=\dfrac{11}{6}\)
d: \(x=\dfrac{4}{9}:\dfrac{5}{3}=\dfrac{4}{9}\cdot\dfrac{3}{5}=\dfrac{12}{45}=\dfrac{4}{15}\)
NV
1
31 tháng 8 2021
a: ta có: \(\left(2x-5\right)\left(x+2\right)-2x\left(x-1\right)=15\)
\(\Leftrightarrow2x^2+4x-5x-10-2x^2+2x=15\)
\(\Leftrightarrow x=25\)
b: Ta có: \(\left(5-2x\right)\left(2x+7\right)=4x^2-25\)
\(\Leftrightarrow4x^2-25+\left(2x-5\right)\left(2x+7\right)=0\)
\(\Leftrightarrow\left(2x-5\right)\left(2x+5+2x+7\right)=0\)
\(\Leftrightarrow\left(2x-5\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-3\end{matrix}\right.\)
c: Ta có: \(x\left(4x-5\right)-\left(2x+1\right)^2=0\)
\(\Leftrightarrow4x^2-5x-4x^2-4x-1=0\)
\(\Leftrightarrow-9x=1\)
hay \(x=-\dfrac{1}{9}\)
25 tháng 8 2021
a) \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1=\left(x^2+3x\right)\left(x^2+3x+2\right)+1=\left(x^2+3x\right)^2+2\left(x^2+3x\right)+1=\left(x^2+3x+1\right)^2\)
b) \(\left(1+x^2\right)\left(1+y^2\right)+4xy+2\left(x+y\right)\left(1+xy\right)=25\Leftrightarrow1+x^2+y^2+x^2y^2+4xy+2\left(x+y\right)\left(1+xy\right)-25=0\Leftrightarrow\left(x+y\right)^2+2\left(x+y\right)\left(1+xy\right)+\left(1+xy\right)^2-25=0\Leftrightarrow\left(x+y+1+xy\right)^2-25=0\Leftrightarrow\left(x+y+xy-24\right)\left(x+y+xy+26\right)=0\)
26 tháng 8 2021
a: Ta có: \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)
\(=\left(x^2+3x\right)\left(x^2+3x+2\right)+1\)
\(=\left(x^2+3x\right)^2+2\left(x^2+3x\right)+1\)
\(=\left(x^2+3x+1\right)^2\)
5 tháng 10 2023
\(b,\left(x+2\right)^2-25\)
\(=\left(x+2\right)^2-5^2\)
\(=\left(x-3\right)\left(x+7\right)\)
\(c,36\left(x-y\right)^2\)
\(=36\left(x^2-2xy+y^2\right)\)
\(=36x^2-72xy+36y^2\)
\(d,x^2+\dfrac{1}{2}x+\dfrac{1}{16}\)
\(=x^2+2.x.\dfrac{1}{4}+\dfrac{1}{4}^2\)
\(=\left(x+\dfrac{1}{4}\right)^2\)
\(e,2x^4y^3-3x^2y^4+5x^3y^4\)
\(=x^2y^3\left(2x^2-3y+5xy\right)\)
Các câu còn lại làm tương tự, chú ý sd HĐT
a) \(\left(x-1\right)-\left(x+3\right)=x-1-x-3=-4\)
b) \(\left(x+1\right)^2=25\)\(\Leftrightarrow\orbr{\begin{cases}x+1=-5\\x+1=5\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-6\\x=4\end{cases}}\)
Vậy \(x=-6\)hoặc \(x=4\)
c) \(\left(x-1\right)\left(5-x\right)>0\)\(\Rightarrow\)\(x-1\)và \(5-x\)cùng âm hoặc dương
TH1: \(\hept{\begin{cases}x-1< 0\\5-x< 0\end{cases}}\Leftrightarrow\hept{\begin{cases}x< 1\\5< x\end{cases}}\Leftrightarrow\hept{\begin{cases}x< 1\\x>5\end{cases}}\)( vô lý )
TH2: \(\hept{\begin{cases}x-1>0\\5-x>0\end{cases}}\Leftrightarrow\hept{\begin{cases}x>1\\5>x\end{cases}}\Leftrightarrow\hept{\begin{cases}x>1\\x< 5\end{cases}}\Leftrightarrow1< x< 5\)
Vậy \(\left(x-1\right)\left(5-x\right)>0\Leftrightarrow1< x< 5\)
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