làm từ câu 39 đến 53 ạ milk cần gấp ạ cảm ơn
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Câu 9:
a) Ta có: \(9x^2-16=0\)
\(\Leftrightarrow\left(3x-4\right)\left(3x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=-\dfrac{4}{3}\end{matrix}\right.\)
b) Ta có: \(4x^2=13\)
\(\Leftrightarrow x^2=\dfrac{13}{4}\)
\(\Leftrightarrow x\in\left\{\dfrac{\sqrt{13}}{2};-\dfrac{\sqrt{13}}{2}\right\}\)
c) Ta có: \(2x^2+9=0\)
\(\Leftrightarrow2x^2=-9\)(Vô lý)
d) Ta có: \(-x^2+324=0\)
\(\Leftrightarrow x^2=324\)
\(\Leftrightarrow\left[{}\begin{matrix}x=18\\x=-18\end{matrix}\right.\)
1.A
2.A
3.B
4.C
5.B
6.C
7.A
8.A
9.B
10.A
11.B
12.A
13.C
14.B
15.B
16.A
17.A
18.A
19.A
20.C
a: UM=AU=2,5/2=1,25cm
VA=VE=AE/2=1,25cm
b: UV=1,25+1,25=2,5cm
Câu 15:
1: Ta có: \(\sqrt{2x+5}=\sqrt{1-x}\)
\(\Leftrightarrow2x+5=1-x\)
\(\Leftrightarrow2x+x=1-5\)
\(\Leftrightarrow3x=-4\)
hay \(x=-\dfrac{4}{3}\)
2: Ta có: \(\sqrt{2x-1}=\sqrt{x-1}\)
\(\Leftrightarrow2x-1=x-1\)
\(\Leftrightarrow x=0\)(loại
3: Ta có: \(\sqrt{x^2-x}=\sqrt{3x-5}\)
\(\Leftrightarrow x^2-x=3x-5\)
\(\Leftrightarrow x^2-4x+5=0\)
\(\Leftrightarrow\left(x-2\right)^2+1=0\)(vô lý
4: Ta có: \(\sqrt{2x^2-3}=\sqrt{4x-3}\)
\(\Leftrightarrow2x^2=4x\)
\(\Leftrightarrow2x^2-4x=0\)
\(\Leftrightarrow2x\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=2\left(nhận\right)\end{matrix}\right.\)
5: Ta có: \(\sqrt{x^2-x}=\sqrt{3-x}\)
\(\Leftrightarrow x^2=3\)
\(\Leftrightarrow x\in\left\{\sqrt{3};-\sqrt{3}\right\}\)
\(1,=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\\ 2,=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\\ 3,=2y\left(y^2+4y+4\right)=2y\left(y+2\right)^2\\ 4,=2\left(x^2+2x+1-y^2\right)=2\left[\left(x+1\right)^2-y^2\right]\\ =2\left(x+y+1\right)\left(x-y+1\right)\\ 5,=16-\left(x-y\right)^2=\left(4-x+y\right)\left(4+x-y\right)\)
2) \(=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\)
3) \(=2y\left(y^2+4y+4\right)=2y\left(y+2\right)^2\)
4) \(=2\left[\left(x^2+2x+1\right)-y^2\right]=2\left[\left(x+1\right)^2-y^2\right]\)
\(=2\left(x+1-y\right)\left(x+1+y\right)\)
5) \(=16-\left(x^2-2xy+y^2\right)=16-\left(x-y\right)^2\)
\(=\left(4-x+y\right)\left(4+x-y\right)\)
39) Ta có: \(\sqrt{49-5\sqrt{96}}-\sqrt{49+5\sqrt{96}}\)
\(=\sqrt{49-20\sqrt{6}}-\sqrt{49+20\sqrt{6}}\)
\(=5-2\sqrt{6}-5-2\sqrt{6}\)
\(=-4\sqrt{6}\)
40) Ta có: \(\sqrt{35+12\sqrt{6}}-\sqrt{35-12\sqrt{6}}\)
\(=3\sqrt{3}+2\sqrt{2}-3\sqrt{3}+2\sqrt{2}\)
\(=4\sqrt{2}\)
41) Ta có: \(\sqrt{13+2\sqrt{42}}+\sqrt{13-2\sqrt{42}}\)
\(=\sqrt{7}+\sqrt{6}+\sqrt{7}-\sqrt{6}\)
\(=2\sqrt{7}\)