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a, \(2\sqrt{3}-\sqrt{4+x^2}=0\Leftrightarrow\sqrt{4+x^2}=2\sqrt{3}\)
\(\Leftrightarrow x^2+4=12\Leftrightarrow x^2=8\Leftrightarrow x=\pm2\sqrt{2}\)
b, \(\sqrt{16x+16}-\sqrt{9x+9}=0\)ĐK : x >= -1
\(\Leftrightarrow4\sqrt{x+1}-3\sqrt{x+1}=0\Leftrightarrow\sqrt{x+1}=0\Leftrightarrow x+1=0\Leftrightarrow x=-1\)
c, \(\sqrt{4\left(x+2\right)^2}=8\Leftrightarrow2\left|x+2\right|=8\Leftrightarrow\left|x+2\right|=4\)
TH1 : \(x+2=4\Leftrightarrow x=2\)
TH2 : \(x+2=-4\Leftrightarrow x=-6\)
c: Ta có: \(\sqrt{4\left(x+2\right)^2}=8\)
\(\Leftrightarrow\left|x+2\right|=4\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=4\\x+2=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-6\end{matrix}\right.\)
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Đề 1:
Bài 1:
\(a,=\sqrt{\left(\sqrt{7}+1\right)^2}-\left|-1+\sqrt{7}\right|=\sqrt{7}+1-\sqrt{7}+1=2\\ b,=2\sqrt{2}-4\sqrt{2}-5\sqrt{2}+\dfrac{\sqrt{2}}{2}=\dfrac{\sqrt{2}}{2}-7\sqrt{2}=\dfrac{-13\sqrt{2}}{\sqrt{2}}\)
Bài 2:
\(PT\Leftrightarrow\sqrt{\left(x-\dfrac{1}{2}\right)^2}=\dfrac{1}{2}\Leftrightarrow\left|x-\dfrac{1}{2}\right|=\dfrac{1}{2}\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}+\dfrac{1}{2}=1\\x=-\dfrac{1}{2}+\dfrac{1}{2}=0\end{matrix}\right.\)
Bài 3:
\(a,M=\dfrac{a-2\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\dfrac{2\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}=\dfrac{2\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}-1\right)^2\left(\sqrt{a}+1\right)}=\dfrac{2}{\sqrt{a}+1}\\ b,M< 1\Leftrightarrow\dfrac{2}{\sqrt{a}+1}-1< 0\Leftrightarrow\dfrac{1-\sqrt{a}}{\sqrt{a}+1}< 0\\ \Leftrightarrow1-\sqrt{a}< 0\left(\sqrt{a}+1>0\right)\\ \Leftrightarrow a>1\)
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1) \(HPT.\) \(\Leftrightarrow\left\{{}\begin{matrix}6\sqrt{x}+4\sqrt{y}=32.\\6\sqrt{x}-9\sqrt{y}=-33.\end{matrix}\right.\) \(\left(x\ge0;y\ge0\right).\)
\(\Leftrightarrow\left\{{}\begin{matrix}3\sqrt{x}+2\sqrt{y}=16.\\13\sqrt{y}=65.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x}=2.\\\sqrt{y}=5.\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=4.\\y=25.\end{matrix}\right.\) (TM).
2) \(HPT.\Leftrightarrow\) \(\left\{{}\begin{matrix}3\left|x\right|+12\left|y\right|=54.\\3\left|x\right|+\left|y\right|=10.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left|x\right|+4\left|y\right|=18.\\\left|y\right|=4.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left|x\right|=2.\\\left|y\right|=4.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=2.\\x=-2.\end{matrix}\right.\\\left[{}\begin{matrix}y=4.\\y=-4.\end{matrix}\right.\end{matrix}\right.\)
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DK\(x\ge\sqrt[3]{2}\)
\(pt\Leftrightarrow\sqrt[3]{x^2-1}-2+x-3-\left(\sqrt{x^3-2}-5\right)=0\)
\(\Leftrightarrow\frac{x^2-9}{\sqrt[3]{x^2-1}+2}+x-3-\frac{x^3-27}{\sqrt{x^3-2}+5}=0\)
\(\Leftrightarrow\left(x-3\right)\left(\frac{x+3}{\sqrt[3]{x^2-1}+2}+1-\frac{x^2+3x+9}{\sqrt{x^3-2}+5}\right)=0\)
\(\Leftrightarrow x=3\)
Vay...
mk lm đến đấy r còn phần đánh giá bên trong biểu thức nx cơ
![](https://rs.olm.vn/images/avt/0.png?1311)
Bạn nên chịu khó gõ đề ra khả năng được giúp sẽ cao hơn.
Câu h của em đây nhé
h, ( 1 + \(\dfrac{3-\sqrt{3}}{\sqrt{3}-1}\)).(1 - \(\dfrac{3+\sqrt{3}}{\sqrt{3}+1}\))
= \(\dfrac{\sqrt{3}-1+3-\sqrt{3}}{\sqrt{3}-1}\).\(\dfrac{\sqrt{3}+1-3-\sqrt{3}}{\sqrt{3}+1}\)
= \(\dfrac{2}{\sqrt{3}-1}\).\(\dfrac{-2}{\sqrt{3}+1}\)
= \(\dfrac{-4}{2}\)
= -2
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\(1,ĐK:x\ge2\\ PT\Leftrightarrow\sqrt{3x-6}+x-2-\left(\sqrt{2x-3}-1\right)=0\\ \Leftrightarrow\dfrac{3\left(x-2\right)}{\sqrt{3x-6}}+\left(x-2\right)-\dfrac{2\left(x-2\right)}{\sqrt{2x-3}+1}=0\\ \Leftrightarrow\left(x-2\right)\left(\dfrac{3}{\sqrt{3x-6}}-\dfrac{2}{\sqrt{2x-3}+1}+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\\dfrac{3}{\sqrt{3x-6}}-\dfrac{2}{\sqrt{2x-3}+1}+1=0\left(1\right)\end{matrix}\right.\)
Với \(x>2\Leftrightarrow-\dfrac{2}{\sqrt{2x-3}+1}>-\dfrac{2}{1+1}=-1\left(3x-6\ne0\right)\)
\(\Leftrightarrow\left(1\right)>0-1+1=0\left(vn\right)\)
Vậy \(x=2\)
\(2,ĐK:x\ge-1\)
Đặt \(\left\{{}\begin{matrix}\sqrt{x+1}=a\\\sqrt{x^2-x+1}=b\end{matrix}\right.\left(a,b\ge0\right)\Leftrightarrow a^2+b^2=x^2+2\)
\(PT\Leftrightarrow2a^2+2b^2-5ab=0\\ \Leftrightarrow\left(a-2b\right)\left(2a-b\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}a=2b\\b=2a\end{matrix}\right.\)
Với \(a=2b\Leftrightarrow x+1=4x^2-4x+4\left(vn\right)\)
Với \(b=2a\Leftrightarrow4x+4=x^2-x+1\Leftrightarrow x^2-5x-3=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5+\sqrt{37}}{2}\left(tm\right)\\x=\dfrac{5-\sqrt{37}}{2}\left(tm\right)\end{matrix}\right.\)
Vậy ...
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ĐK: \(x\ge\dfrac{5}{3}\)
Ta có: \(\sqrt{2x+5}=2+\sqrt{3x-5}\)
\(\Leftrightarrow2x+5=4+3x-5+4\sqrt{3x-5}\)
\(\Leftrightarrow6-x=4\sqrt{3x-5}\) ĐK: x≤6
\(\Leftrightarrow36-12x+x^2=48x-80\)
\(\Leftrightarrow x^2-60x+116=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-58\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=58\end{matrix}\right.\)
So với điều kiện thì phương trình có nghiệm duy nhất là x = 2
\(ĐK:x\ge\dfrac{5}{3}\\ PT\Leftrightarrow\left(\sqrt{2x+5}-3\right)-\left(\sqrt{3x-5}-1\right)=0\\ \Leftrightarrow\dfrac{2x-4}{\sqrt{2x+5}+3}-\dfrac{3x-6}{\sqrt{3x-5}+1}=0\\ \Leftrightarrow\left(x-2\right)\left(\dfrac{2}{\sqrt{2x+5}+3}-\dfrac{3}{\sqrt{3x-5}+1}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\\dfrac{2}{\sqrt{2x+5}+3}=\dfrac{3}{\sqrt{3x-5}+1}\left(1\right)\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow2\sqrt{3x-5}+2=3\sqrt{2x+5}+9\\ \Leftrightarrow2\sqrt{3x-5}=7+3\sqrt{2x+5}\\ \Leftrightarrow4\left(3x-5\right)=49+9\left(2x+5\right)+42\sqrt{2x+5}\\ \Leftrightarrow12x-20=49+18x+45+42\sqrt{2x+5}\\ \Leftrightarrow-6x-144=42\sqrt{2x+5}\)
Vì \(x\ge\dfrac{5}{3}>0\Leftrightarrow-6x-144< 0< 42\sqrt{2x+5}\)
Do đó (1) vô nghiệm
Vậy PT có nghiệm \(x=2\)
\(1:x< 0\left(B\right)\)
\(2:\left(D\right)\)
\(3:x< 2021\left(C\right)\)
\(4:x\ge15\left(D\right)\)
\(5:\)để pt có nghĩa thì 2x-5>0
\(2x>5< =>x>\frac{5}{2}\)
chọn (C)
\(6:\frac{1}{2}\sqrt{20}-\sqrt{\left(2-\sqrt{5}\right)^2}\)
\(\frac{1}{2}\sqrt{20}-\sqrt{5}+2\)
\(\sqrt{5}-\sqrt{5}+2=2\)
chọn (B)
\(7:\frac{6xy^2}{x^2-y^2}\sqrt{\frac{\left(x-y\right)^2}{\left(3xy^2\right)^2}}\)
\(\frac{6xy^2}{x^2-y^2}\frac{x-y}{3xy^2}\)
\(\frac{2}{x+y}\)
chọn (B)
\(8:\left(1+\frac{3-\sqrt{3}}{\sqrt{3}-1}\right)\left(\frac{3+\sqrt{3}}{\sqrt{3}+1}-1\right)\)
\(\left(1+\frac{\sqrt{3}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}\right)\left(\frac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}-1\right)\)
\(\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)\)
\(\sqrt{3}^2-1^2=3-1=2\)
chọn (D)
\(9:M=\left|1-\sqrt{3}\right|+\left|1-\sqrt{3}\right|\)
\(M=\sqrt{3}-1+\sqrt{3}-1\)
\(M=2\sqrt{3}-2\)
chọn (A)
\(10:\sqrt{4+\sqrt{x^2-1}}=2\)
\(4+\sqrt{x^2-1}=2^2=4\)
\(\sqrt{x^2-1}=0\)
\(x^2-1=0< =>x=1\)
chọn (A)
1 B
2 D
3 C
4 D
5 C
6 B
7 B
8 D
9 D
10 B