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1 You should not wear shorts when going to the pagoda
2 At Tet, our house is more beautifully decorated than during the year
3 Sitting in front of a computer all day can cause health problems
4 Snow White is very kind to people and animals
5 Hung King Temple festival has been a public holiday in VN since 2007
III
1 Last night, we were having dinner when the telephone rang
2 Life in the countryside has changed a lot over the past ten years
3 Nam doesn't mind listening to classical music
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a: Xét ΔABK vuông tại K và ΔACK vuông tại K có
AB=AC
AK chung
=>ΔABK=ΔACK
=>KB=KC
b: BK=căn 15^2-12^2=9cm
=>BC=9*2=18cm
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Bài 13:
$6-2\sqrt{5}=5-2\sqrt{5}.\sqrt{1}+1$
$=(\sqrt{5}-1)^2$
Tương tự: $6+2\sqrt{5}=(\sqrt{5}+1)^2$
Do đó:
$M=\sqrt{(\sqrt{5}+1)^2}-\sqrt{(\sqrt{5}-1)^2}$
$=|\sqrt{5}+1|-|\sqrt{5}-1|=(\sqrt{5}+1)-(\sqrt{5}-1)$
$=2$
Bài 14:
a.
$M=\sqrt{4+2\sqrt{4}.\sqrt{5}+5}-\sqrt{4-2\sqrt{4}.\sqrt{5}+5}$
$=\sqrt{(\sqrt{4}+\sqrt{5})^2}-\sqrt{(\sqrt{4}-\sqrt{5})^2}$
$=|\sqrt{4}+\sqrt{5}|-|\sqrt{4}-\sqrt{5}|$
$=2+\sqrt{5}-(\sqrt{5}-2)=4$
b.
$N=\sqrt{7-2\sqrt{7}+1}-\sqrt{7+2\sqrt{7}+1}$
$=\sqrt{(\sqrt{7}-1)^2}-\sqrt{(\sqrt{7}+1)^2}$
$=|\sqrt{7}-1|-|\sqrt{7}+1|$
$=(\sqrt{7}-1)-(\sqrt{7}+1)=-2$
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a: Xét ΔAHB vuông tại H và ΔAHC vuông tại H có
AH chung
AB=AC
=>ΔAHB=ΔAHC
b: Xét ΔCHM vuông tại H và ΔCNM vuông tại N có
CM chung
góc HCM=góc NCM
=>ΔCHM=ΔCNM
=>CN=CH
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\(\left(x+1\right)\left(2x-2\right)-3>-5x-\left(2x+1\right)\left(3x-x\right)\)
\(\Leftrightarrow2x^2-2x+2x-2-3>-5x-\left(6x^2-2x^2+3x-x\right)\)
\(\Leftrightarrow2x^2-2x+2x-5>-5x-6x^2+2x^2-3x+x\)
\(\Leftrightarrow2x^2-5+5x+6x^2-2x^2+3x-x>0\)
\(\Leftrightarrow6x^2-2x>5\)
\(\Leftrightarrow2x\left(3x-1\right)>5\)
\(\Leftrightarrow\left[{}\begin{matrix}2x>5\\3x-1>5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{5}{2}\\x>2\end{matrix}\right.\)
Đặt \(S=\frac{x^2}{5}+\frac{3}{2}\)
Ta có: \(x^2\ge0\forall x\)
\(\Rightarrow\frac{x^2}{5}\ge0\)
\(\Rightarrow\frac{x^2}{5}+\frac{3}{2}\ge\frac{3}{2}\)
hay \(MinS=\frac{3}{2}\)
Dấu "=" xảy ra khi \(x^2=0\Rightarrow x=0\)
Vậy \(MinS=\frac{3}{2}\) tại \(x=0\).