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9:
a: BC^2=AB^2+AC^2
=>ΔABC vuông tại A
b: Xét ΔBAD vuông tại A và ΔBED vuông tại E có
BD chung
góc ABD=góc EBD
=>ΔBAD=ΔBED
=>DA=DE và BA=BE
c: DA=DE
DA<DF
=>DE<DF
\(=\dfrac{3}{2}-\dfrac{2}{21}-\dfrac{7}{12}+\left[\dfrac{15}{21}-\dfrac{1}{3}+\dfrac{5}{4}-\dfrac{2}{7}-\dfrac{1}{3}\right]\)
=11/12-2/21+5/7-2/3+5/4-2/7
=11/12-2/3+5/4-2/21+3/7
=11/12-8/12+15/12-2/21+9/21
=18/12+7/21
=3/2+1/3
=9/6+2/6=11/6
\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\left[\dfrac{15}{21}-\left(\dfrac{1}{3}-\dfrac{5}{4}\right)-\left(\dfrac{2}{7}+\dfrac{1}{3}\right)\right]\right\}\)
\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\left[\dfrac{15}{21}-\left(-\dfrac{11}{12}\right)-\dfrac{13}{21}\right]\right\}\)
\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\dfrac{85}{84}\right\}\)
\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left(-\dfrac{3}{7}\right)\)
\(B=\dfrac{11}{6}\)
1) \(\left(\dfrac{-13}{17}-\dfrac{31}{52}\right)-\left(\dfrac{73}{52}-\dfrac{13}{17}+\dfrac{5}{6}\right)-\dfrac{3}{4}\)
\(=\dfrac{-13}{17}-\dfrac{31}{52}-\dfrac{73}{52}+\dfrac{13}{17}-\dfrac{5}{6}-\dfrac{3}{4}\)
\(=\left(\dfrac{-13}{17}+\dfrac{13}{17}\right)-\left(\dfrac{31}{52}+\dfrac{73}{52}\right)-\left(\dfrac{5}{6}+\dfrac{3}{4}\right)\)
\(=0-2-\dfrac{19}{12}\)
\(=-2-\dfrac{19}{12}\)
\(=\dfrac{-43}{12}\)
a) \(4\sqrt{x}=8\Leftrightarrow\sqrt{x}=2\Leftrightarrow x=4\)
b) \(\left(x-1\right)^2=9\Leftrightarrow x-1=3\Leftrightarrow x=4\)
c: Áp dung tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{x}{4}=\dfrac{y}{9}=\dfrac{x+y}{4+9}=3\)
Do đó: x=12; y=27
Bài 5:
a) \(x:\left(-\dfrac{1}{2}\right)^3=-\dfrac{1}{2}\)
\(\Rightarrow x=\left(-\dfrac{1}{2}\right)^3\cdot\left(-\dfrac{1}{2}\right)\)
\(\Rightarrow x=\left(\dfrac{1}{2}\right)^4=\dfrac{1}{16}\)
b) \(\left(\dfrac{3}{4}\right)^5\cdot x=\left(\dfrac{3}{4}\right)^7\)
\(\Rightarrow x=\left(\dfrac{3}{4}\right)^7:\left(\dfrac{3}{4}\right)^5\)
\(\Rightarrow x=\left(\dfrac{3}{4}\right)^2=\dfrac{9}{16}\)
c) \(\left(\dfrac{2}{3}\right)^5:x=\left(\dfrac{2}{3}\right)^3\)
\(\Rightarrow x=\left(\dfrac{2}{5}\right)^5:\left(\dfrac{2}{3}\right)^3\)
\(\Rightarrow x=\left(\dfrac{2}{5}\right)^2=\dfrac{4}{25}\)
d) \(\dfrac{25}{5^x}=5\)
\(\Rightarrow5^x\cdot5=25\)
\(\Rightarrow5^{x+1}=25\)
\(\Rightarrow5^{x+1}=5^2\)
\(\Rightarrow x+1=2\)
\(\Rightarrow x=2-1=1\)
e) \(\left(-\dfrac{1}{3}\right)^{x-5}=\dfrac{1}{81}\)
\(\Rightarrow\left(-\dfrac{1}{3}\right)^{x-5}=\left(-\dfrac{1}{3}\right)^4\)
\(\Rightarrow x-5=4\)
\(\Rightarrow x=4+5=9\)
g) \(\left(2x-3\right)^2=9\)
\(\Rightarrow\left(2x-3\right)=3^2\)
\(\Rightarrow2x-3=3\)
\(\Rightarrow2x=6\)
\(\Rightarrow x=\dfrac{6}{2}=3\)
h) \(\left(x+5\right)^3=64\)
\(\Rightarrow\left(x+5\right)^3=4^3\)
\(\Rightarrow x+5=4\)
\(\Rightarrow x=4-5=-1\)
i) \(2^{3x+2}=4^{x+5}\)
\(\Rightarrow2^{3x+2}=\left(2^2\right)^{x+5}\)
\(\Rightarrow2^{3x+2}=2^{2x+10}\)
\(\Rightarrow3x+2=2x+10\)
\(\Rightarrow3x-2x=10-2\)
\(\Rightarrow x=8\)
k) \(5^{x+1}-5^x=500\)
\(\Rightarrow\left(5-1\right)\cdot5^x=500\)
\(\Rightarrow4\cdot5^x=500\)
\(\Rightarrow5^x=125\)
\(\Rightarrow5^x=5^3\)
\(\Rightarrow x=3\)
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