ĐKXĐ: \(x\ne a;x\ne-2\)

PT\(\Leftrightarrow\frac{\left(x+a\right)\left(x-a\right)}{\left(x+2\right)\left(x-a\right)}+\frac{\left(x-2\right)\left(x+2\right)}{\left(x+2\right)\left(x-a\right)}=2\)

\(\Rightarrow\left(x+a\right)\left(x-a\right)+\left(x-2\right)\left(x+2\right)=2\left(x+2\right)\left(x-a\right)\)

\(\Leftrightarrow x^2-a^2+x^2-4=2\left(x^2+2x-ax-2a\right)\)

\(\Leftrightarrow2x^2-a^2-4=2x^2+4x-2ax-4a\)

\(\Leftrightarrow-a^2-4=\left(4-2a\right)x-4a\)

\(\Leftrightarrow\left(2a-4\right)x=a^2-4a+4\)

\(\Leftrightarrow2\left(a-2\right)x=\left(a-2\right)^2\)

Nếu a=2 thì PT có vô số nghiệm khác 2 và -2

Nếu a khác 2 thì PY có 1 nghiệm \(x=\frac{a-2}{2}\)với ĐK \(\hept{\begin{cases}\frac{a-2}{2}\ne-2\\\frac{a-2}{2}\ne a\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}a-2\ne-4\\a-2\ne2a\end{cases}}\)

\(\Leftrightarrow a\ne-2\)

Vậy nếu a=2 thì PT có vô số nghiệm khác \(\pm\)2.Nếu a \(\ne\pm\)2 thì PT có 1 nghiệm \(x=\frac{a-2}{2}\).Nếu a=-2 thì PT vô nghiệm.
 

bằng 2

2

giúp mk vs, ko cần dài lắm đâu

bn ra đây hỏi làm gì bn chép mạng có phải nhanh hơn ko

\(5a^2+5b^2+8ab-2a+2b+2=0\)

\(\Leftrightarrow4a^2+4b^2+8ab+a^2-2a+1+b^2-2b+1=0\)

\(\Leftrightarrow\left(2a+2b\right)^2+\left(a-1\right)^2+\left(b+1\right)^2=0\)

\(\Leftrightarrow\hept{\begin{cases}2a+2b=0\\a-1=0\\b+1=0\end{cases}\Leftrightarrow\hept{\begin{cases}a\cdot1+2\left(-1\right)=0\left(tm\right)\\a=1\\b=-1\end{cases}}}\)

Thay a, b vào B ta được :

\(B=\left(1-1\right)^{2018}+\left(1-2\right)^{2019}+\left(-1+1\right)^{2020}\)

\(B=0^{2018}+\left(-1\right)^{2019}+0^{2020}\)

\(B=-1\)

Dòng 2 là \(+2b\)nhé mình bấm lộn :)

P/s: ko chắc 

\(P=\frac{x^2-x+1}{x^2+x+1}\)

\(P=\frac{x^2}{x^2+x+1}-\frac{x}{x^2+x+1}+\frac{1}{x^2+x+1}\)

\(P=x^2\cdot\frac{1}{x^2+x+1}-x\cdot\frac{1}{x^2+x+1}+\frac{1}{x^2+x+1}\)

\(P=\frac{1}{x^2+x+1}\left(x^2-x+1\right)\)

\(P=\frac{1}{x^2+x+1}\left[x^2-2\cdot x\cdot\frac{1}{2}+\frac{1}{4}+\frac{3}{4}\right]\)

\(P=\frac{1}{x^2+x+1}\left[\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\right]\)

\(P=\frac{1}{x^2+x+1}\cdot\left(x-\frac{1}{2}\right)^2+\frac{1}{x^2+x+1}\cdot\frac{3}{4}\)

Vì \(\frac{1}{x^2+x+1}\cdot\left(x-\frac{1}{2}\right)^2\ge0\forall x\)

\(\Rightarrow P\ge\frac{1}{x^2+x+1}\cdot\frac{3}{4}\)

Dấu "=" xảy ra \(\Leftrightarrow\frac{1}{x^2+x+1}\cdot\left(x-\frac{1}{2}\right)^2\Leftrightarrow x-\frac{1}{2}=0\Leftrightarrow x=\frac{1}{2}\)

Vậy...

dễ hơn nè

Ta thấy x² + x + 1 > 0

Ta có : 2 ( x - 1 )² \(\ge\)0 \(\Rightarrow\)2x² - 4x + 2 \(\ge\)0 \(\Rightarrow\)3 ( x² - x + 1 ) \(\ge\)x² + x + 1

\(\Rightarrow\frac{x^2-x+1}{x^2+x+1}\ge\frac{1}{3}\) . Dấu " = " xảy ra  \(\Leftrightarrow\)x = 1 

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