tim x\(\in\)z
(4x+1)\(⋮\)(2x+2)
K
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K
2 tháng 8 2021
Ta có:
D=2x2+3y2+4xy−8x−2y+18C=2x2+3y2+4xy−8x−2y+18
D=2(x2+2xy+y2)+y2−8x−2y+18C=2(x2+2xy+y2)+y2−8x−2y+18
D=2[(x+y)2−4(x+y)+4]+(y2+6y+9)+1C=2[(x+y)2−4(x+y)+4]+(y2+6y+9)+1
D=2(x+y−2)2+(y+3)2+1≥1C=2(x+y−2)2+(y+3)2+1≥1
Dấu "=" xảy ra ⇔x+y=2⇔x+y=2và y=−3y=−3
Hay x = 5 , y = -3
Đc chx bạn
19 tháng 9 2019
\(a,4x^2+9y^2+4x-24y+17=0\)
\(\Rightarrow\left(4x^2+4x+1\right)+\left(9y^2-24y+16\right)=0\)
\(\Rightarrow\left(2x+1\right)^2+\left(3y-4\right)^2=0\)
\(\left(2x+1\right)^2\ge0;\left(3y-4\right)^2\ge0\)
\(\Rightarrow\hept{\begin{cases}\left(2x+1\right)^2=0\\\left(3y-4\right)^2=0\end{cases}\Rightarrow\hept{\begin{cases}2x+1=0\\3y-4=0\end{cases}\Rightarrow}\hept{\begin{cases}x=-\frac{1}{2}\\y=\frac{4}{3}\end{cases}}}\)
KN
18 tháng 8 2021
a. ĐKXĐ : \(x\ne\frac{1}{2};\frac{5}{2};4;-\frac{3}{2};\frac{1\pm\sqrt{43}}{2}\)
\(A=\left(\frac{2x-3}{4x^2-12x+5}+\frac{3x-8}{13x-2x^2-20}-\frac{3}{2x-1}\right):\frac{21+2x-2x^2}{4x^2+4x-3}+\)
\(=\left(\frac{2x-3}{\left(2x-1\right)\left(2x-5\right)}-\frac{3x-8}{\left(2x-5\right)\left(x-4\right)}-\frac{3}{2x-1}\right).\frac{\left(2x-1\right)\left(2x+3\right)}{21+2x-2x^2}+1\)
\(=\frac{\left(2x-3\right)\left(x-4\right)-\left(3x-8\right)\left(2x-1\right)-3\left(2x-5\right)\left(x-4\right)}{\left(2x-1\right)\left(2x-5\right)\left(x-4\right)}.\frac{\left(2x-1\right)\left(2x+3\right)}{21+2x-2x^2}+1\)
\(=\frac{-10x^2+47x-56}{\left(2x-5\right)\left(x-4\right)}.\frac{2x+3}{-2x^2+2x+21}+1\) số to wa
\(4x+1⋮2x+2\)
\(\Rightarrow4x+4-3⋮2x+2\)
\(\Rightarrow2\left(2x+2\right)-3⋮2x+2\)
\(2\left(2x+2\right)⋮2x+2\)
\(\Rightarrow3⋮2x+2\)
\(\Rightarrow2x+2\inƯ\left(3\right)\)
\(\Rightarrow2x+2\in\left\{-1;1;-3;3\right\}\)
\(\Rightarrow2x\in\left\{-3;-1;-5;1\right\}\)
\(\Rightarrow x\in\left\{-1,5;-0,5;-2,5;0,5\right\}\) mà x thuộc Z
\(\Rightarrow x\in\varnothing\)
\(\frac{4x+1}{2x+2}=\frac{2\left(2x+2\right)-3}{2x+2}=2-\frac{3}{2x+2}\)
\(\Rightarrow3⋮\left(2x+2\right)\Rightarrow2x+2\inƯ\left(3\right)=\left\{1;3;-1;-3\right\}\)
Nếu 2x+2=1 => 2x=-1 => x=-1/2
Nếu 2x+2=3 => 2x=1 => x=1/2
Nếu 2x+2=-1 => 2x=-3 => x=-3/2
Nếu 2x+2=-3 => 2x=-5 => x = -5/2
Vậy x = {-1/2 ; 1/2 ; -3/2 ; -5/2} thì 4x+1 chia hết cho 2x+2