5/6+(-14)/6
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a: \(=\dfrac{5}{14}\left(\dfrac{2}{9}+\dfrac{7}{9}+1\right)=\dfrac{5}{14}\cdot2=\dfrac{5}{7}\)
b: \(=\dfrac{6}{8}\left(\dfrac{6}{7}-6\right)=\dfrac{6}{8}\cdot\dfrac{-36}{7}=\dfrac{-216}{56}=\dfrac{-27}{7}\)
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ví dụ 1 bài 2x-x2
bài giải: -(x2+2x)
=-(x2-2x)
=-(x2-2x.5/2 +25/4 - 25/4)
=-(x-5/2)-25/4<25/4
=25/4+(x-5/2)<25
=>x=5/2
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A = \(\frac{1}{5\times6}+\frac{3}{6\times9}+\frac{5}{9\times14}+\frac{7}{14\times21}+\frac{9}{21\times30}\)
A = \(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{21}+\frac{1}{21}-\frac{1}{30}\)
A = \(1-\frac{1}{30}\)
A = \(\frac{29}{30}\)
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\(\frac{14-6\sqrt{5}+8}{\sqrt{14-6\sqrt{5}}+1}=\frac{22-6\sqrt{5}}{\sqrt{\left(3-\sqrt{5}\right)^2}+1}=\frac{22-6\sqrt{5}}{4-\sqrt{5}}=\frac{\left(22-6\sqrt{5}\right)\left(4+\sqrt{5}\right)}{16-5}=\frac{58-2\sqrt{5}}{11}\)
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\(\sqrt{14-6\sqrt{5}}+\sqrt{14+6\sqrt{5}}=\sqrt{9-2.3\sqrt{5}+5}+\sqrt{9+2.3\sqrt{5}+5}\)
\(=\sqrt{\left(3-\sqrt{5}\right)^2}+\sqrt{\left(3+\sqrt{5}\right)^2}=3-\sqrt{5}+3+\sqrt{5}\)
\(=6\)
\(\dfrac{5}{6}+\dfrac{-14}{6}\)
\(=\dfrac{5+\left(-14\right)}{6}\)
\(=\dfrac{5-14}{6}\)
\(=\dfrac{-9}{6}\)
\(=\dfrac{-3}{2}\)