MN GIÚP E BÀI 2,7,8 VỚI Ạ. GIẢI CHI TIẾT CÁCH LÀM DÙM E.
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Câu 5:
\(\Leftrightarrow-x^2+7x-9+2x-9=0\)
\(\Leftrightarrow x^2-9x+18=0\)
=>x=3
=>Chọn A
40: Ta có: \(A=27x^3+8y^3-3x-2y\)
\(=\left(3x+2y\right)\left(9x^2-6xy+4y^2\right)-\left(3x+2y\right)\)
\(=\left(3x+2y\right)\left(9x^2-6xy+4y^2-1\right)\)
Ta có : \(f\left(2\right)=2a+b-6\)
\(\lim\limits_{x\rightarrow2^+}\dfrac{x-\sqrt{x+2}}{x^2-4}=\lim\limits_{x\rightarrow2^+}\dfrac{x^2-x-2}{\left(x-2\right)\left(x+2\right)\left(x+\sqrt{x+2}\right)}\)
\(=\lim\limits_{x\rightarrow2^+}\dfrac{x+1}{\left(x+2\right)\left(x+\sqrt{x+2}\right)}=\dfrac{3}{16}\)
\(\lim\limits_{x\rightarrow2^-}x^2+ax+3b=4+2a+3b\)
H/s liên tục tại điểm x = 2 \(\Leftrightarrow\dfrac{3}{16}=2a+3b+4=2a+b-6\)
Suy ra : \(a=\dfrac{179}{32};b=-5\) => t = a + b = 19/32 . Chọn C
ĐKXĐ: \(x\notin\left\{0;-9\right\}\)
Ta có: \(\dfrac{1}{x+9}-\dfrac{1}{x}=\dfrac{1}{5}+\dfrac{1}{4}\)
\(\Leftrightarrow\dfrac{20x}{20x\left(x+9\right)}-\dfrac{20\left(x+9\right)}{20x\left(x+9\right)}=\dfrac{4x\left(x+9\right)+5x\left(x+9\right)}{20x\left(x+9\right)}\)
Suy ra: \(4x^2+36x+5x^2+45x=20x-20x-180\)
\(\Leftrightarrow9x^2+81x+180=0\)
\(\Leftrightarrow x^2+9x+20=0\)
\(\Leftrightarrow x^2+4x+5x+20=0\)
\(\Leftrightarrow x\left(x+4\right)+5\left(x+4\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\left(nhận\right)\\x=-5\left(nhận\right)\end{matrix}\right.\)
Vậy: S={-4;-5}
Hướng làm:
Thấy cả tử mẫu cộng lại đều bằng 2021 → Cộng thêm 1 rồi quy đồng với mỗi phân thức
\(\dfrac{x+2}{2019}+1+\dfrac{x+3}{2018}+1=\dfrac{x+4}{2017}+1+\dfrac{x}{2021}+1\\ \Leftrightarrow\dfrac{x+2021}{2019}+\dfrac{x+2021}{2018}-\dfrac{x+2021}{2017}-\dfrac{x+2021}{2021}=0\\ \Leftrightarrow\left(x+2021\right)\left(\dfrac{1}{2019}+\dfrac{1}{2018}-\dfrac{1}{2017}-\dfrac{1}{2021}\right)=0\\ \Leftrightarrow x+2021=0\Leftrightarrow x=-2021\)
\(< =>\dfrac{x+2}{2019}+1+\dfrac{x+3}{2018}+1=\dfrac{x+4}{2017}+1+\dfrac{x}{2021}+1\)
\(< =>\dfrac{x+2+2019}{2019}+\dfrac{x+3+2018}{2018}=\dfrac{x+4+2017}{2017}+\dfrac{x+2021}{2021}\)
\(< =>\dfrac{x+2021}{2019}+\dfrac{x+2021}{2018}-\dfrac{x+2021}{2017}-\dfrac{x+2021}{2021}=0\)
\(< =>\left(x+2021\right)\left(\dfrac{1}{2019}+\dfrac{1}{2018}-\dfrac{1}{2017}-\dfrac{1}{2021}=\right)=0\)
\(< =>x+2021=0< =>x=-2021\)
Vậy....
Bài 2: Chọn C
Bài 4:
a: \(\widehat{C}=180^0-80^0-50^0=50^0\)
Xét ΔABC có \(\widehat{A}=\widehat{C}< \widehat{B}\)
nên BC=AB<AC
b: Xét ΔABC có AB<BC<AC
nên \(\widehat{C}< \widehat{A}< \widehat{B}\)
\(\frac{x+2}{2019}+\frac{x+3}{2018}=\frac{x+4}{2017}+\frac{x}{2021}\)
\(\Leftrightarrow\frac{x+2}{2019}+1+\frac{x+3}{2018}+1=\frac{x+4}{2017}+1+\frac{x}{2021}+1\)
\(\Leftrightarrow\frac{x+2021}{2019}+\frac{x+2021}{2018}=\frac{x+2021}{2017}+\frac{x+2021}{2021}\)
\(\Leftrightarrow x+2021=0\)
\(\Leftrightarrow x=-2021\)
Câu 2: C
CÁCH LÀM SAO Ạ.