\(\sqrt{\frac{x+1}{x^2-x+1}}+\sqrt{\frac{x^2-x+1}{x+1}}=2\)
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\(\sqrt{a}+2\sqrt{a}-1+\sqrt{a}-2\sqrt{a}-1\)
\(=2\sqrt{a}-2\)
vậy thôi à??
\(\frac{2}{\sqrt{7}-\sqrt{5}}+\frac{6}{\sqrt{11}+\sqrt{5}}\)
\(=\frac{2\left(\sqrt{7}+\sqrt{5}\right)}{\left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)}+\frac{6\left(\sqrt{11}-\sqrt{5}\right)}{\left(\sqrt{11}+\sqrt{5}\right)\left(\sqrt{11}-\sqrt{5}\right)}\)
\(=\frac{2\left(\sqrt{7}+\sqrt{5}\right)}{7-5}+\frac{6\left(\sqrt{11}-\sqrt{5}\right)}{11-5}\)
\(=\frac{2\left(\sqrt{7}+\sqrt{5}\right)}{2}+\frac{6\left(\sqrt{11}-\sqrt{5}\right)}{6}\)
\(=\sqrt{7}+\sqrt{5}+\sqrt{11}-\sqrt{5}\)
\(=\sqrt{7}+\sqrt{11}\)
\(A=\frac{1}{\sqrt{3}+1}+\frac{1}{\sqrt{3}-1}\)
\(=\frac{\sqrt{3}-1}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}+\frac{\sqrt{3}+1}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\)
\(=\frac{\sqrt{3}-1+\sqrt{3}+1}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\)
\(=\frac{2\sqrt{3}}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\)
\(=\frac{2\sqrt{3}}{3-1}\)
\(=\frac{2\sqrt{3}}{2}\)
\(=\sqrt{3}\)
\(B=\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}\)
\(=\frac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}\left(\sqrt{5}-1\right)}+\frac{\sqrt{5}\left(\sqrt{5}-1\right)}{\sqrt{5}\left(\sqrt{5}+1\right)}\)
\(=\frac{\left(\sqrt{5}+1\right)}{\left(\sqrt{5}-1\right)}+\frac{\left(\sqrt{5}-1\right)}{\left(\sqrt{5}+1\right)}\)
\(=\frac{\left(\sqrt{5}+1\right)^2}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}+\frac{\left(\sqrt{5}-1\right)^2}{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}\)
\(=\frac{5+2\sqrt{5}+1+5-2\sqrt{5}+1}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}\)
\(=\frac{12}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}\)
\(=\frac{12}{5-1}\)
\(=\frac{12}{4}\)
\(=3\)
Bn tự vẽ hình nhé...
a)
AB⊥CD (GT) => CIB =90 độ (1)
AEB=90độ ( góc nt chắn nữa dg tròn) (2)
Từ (1)và(2) tứ giác BEFI nội tiếp
b)
Xét ΔAFC và Δ ACE có
A( góc chung)
C=E( vì 2 góc cùng chắn 2 cung AC và AD bằng nhau)
=>ΔAFC∼Δ ACE
=> AC/AE=AF/AC
=> AE.AF=AC2
\(\sqrt{\frac{x+1}{x^2-x+1}}+\sqrt{\frac{x^2-x+1}{x+1}}=2\)
\(\Leftrightarrow\left(\sqrt{\frac{x+1}{x^2-x+1}}+\sqrt{\frac{x^2-x+1}{x+1}}\right)^2=2^2\)
\(\Leftrightarrow\frac{x+1}{x^2-x+1}+2.\sqrt{\frac{x+1}{x^2-x+1}}.\sqrt{\frac{x^2-x+1}{x+1}}+\frac{x^2-x+1}{x+1}=4\)
\(\Leftrightarrow\frac{x+1}{x^2-x+1}+\frac{x^2-x+1}{x+1}=4-2\)
\(\Leftrightarrow\frac{\left(x+1\right)^2}{\left(x^2-x+1\right)\left(x+1\right)}+\frac{\left(x^2-x+1\right)^2}{\left(x+1\right)\left(x^2-x+1\right)}=2\)
\(\Leftrightarrow\frac{\left(x+1\right)^2+\left(x^2+1-x\right)^2}{x^3+1}=2\)
\(\Leftrightarrow\frac{x^2+2x+1+x^4+1+x^2+2x^2-2x-2x^3}{x^3+1}=2\)
\(\Leftrightarrow x^2+2x+1+x^4+1+x^2+2x^2-2x-2x^3=2\left(x^3+1\right)\)
\(\Leftrightarrow4x^2+2+x^4-2x^3=2x^3+2\)
\(\Leftrightarrow x^4-2x^3-2x^3+4x^2=2-2\)
\(\Leftrightarrow x^4-4x^3+4x^2=0\)
\(\Leftrightarrow x^2\left(x^2-4x+4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2=0\\x^2-4x+4=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\\left(x-2\right)^2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x-2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}\)
Bạn tự tìm ĐKXĐ rồi so sánh kết quả nhé!