Giải phương trình
1.\(\left(\sqrt{1+x}+\sqrt{1-x}\right)\).\(\left(2+2\sqrt{1-x^2}\right)\)\(=8\)
2.\(\left(x+3\right)\sqrt{\left(4-x\right)\left(12+x\right)}\)\(=28-x\)
Những câu hỏi liên quan
Giải phương trình:
\(\frac{2\left(x-\sqrt{3}\right)\left(x-\sqrt{2}\right)}{\left(1-\sqrt{2}\right)\left(1-\sqrt{3}\right)}+\frac{3\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}-\sqrt{3}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{2}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{2}\right)}=3x-1\)
giải phương trình vô tỉ sau
1 ) \(\sqrt{3x^2-1}+\sqrt{x^2-x}-x\sqrt{x^2+1}=\dfrac{1}{2.\sqrt{2}}.\left(7x^2-x+4\right)\)
2) \(\left(x+3\right)\sqrt{\left(4-x\right)\left(x+12\right)}=28-x\)
3) \(x^4+2x^3+2x^2-2x+1=\left(x^3+x\right)\sqrt{\dfrac{1-x^2}{x}}\)
Giải các bất phương trình sau:
a/ \(\sqrt{\left(x-3\right)\left(8-x\right)}+26>-x^2+11x\)
b/ \(\left(x+1\right)\left(x+4\right)< 5\sqrt{x^2+5x+28}\)
GIÚP MÌNH VỚI Ạ!!!
1) \(\sqrt{2-x^2}+\sqrt{2-\dfrac{1}{x^2}}=4-\left(x+\dfrac{1}{x}\right)\)
2) \(x\sqrt{x}+\sqrt{12-x}=2\sqrt{3\left(x^2+1\right)}\)
3) \(\left(x+8\sqrt{x}+4\right)\left(x-\sqrt{x}+4\right)=36x\)
1. ĐKXĐ:...
\(8-2x-\dfrac{2}{x}-2\sqrt{2-x^2}-2\sqrt{2-\dfrac{1}{x^2}}=0\)
\(\Leftrightarrow\left(x^2-2x+1\right)+\left(\dfrac{1}{x^2}-\dfrac{2}{x}+1\right)+\left(2-x^2-2\sqrt{2-x^2}+1\right)+\left(2-\dfrac{1}{x^2}-2\sqrt{2-\dfrac{1}{x^2}}+1\right)=0\)
\(\Leftrightarrow\left(x-1\right)^2+\left(\dfrac{1}{x}-1\right)^2+\left(\sqrt{2-x^2}-1\right)^2+\left(\sqrt{2-\dfrac{1}{x^2}}-1\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\\dfrac{1}{x}-1=0\\\sqrt{2-x^2}-1=0\\\sqrt{2-\dfrac{1}{x^2}}-1=0\end{matrix}\right.\)
\(\Leftrightarrow x=1\)
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2.
ĐKXĐ:...
Ta có:
\(VT=x\sqrt{x}+1.\sqrt{12-x}\le\sqrt{\left(x^2+1\right)\left(x+12-x\right)}=2\sqrt{3\left(x^2+1\right)}\)
Dấu "=" xảy ra khi và chỉ khi: \(x\sqrt{12-x}=\sqrt{x}\)
\(\Leftrightarrow x^3-12x^2+x=0\Rightarrow\left[{}\begin{matrix}x=0\\x=6-\sqrt{35}\\x=6+\sqrt{35}\end{matrix}\right.\)
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3. ĐKXĐ: ...
Với \(x=0\) ko phải nghiệm
Với \(x>0\) pt tương đương:
\(\left(\dfrac{x+8\sqrt{x}+4}{\sqrt{x}}\right)\left(\dfrac{x-\sqrt{x}+4}{\sqrt{x}}\right)=36\)
\(\Leftrightarrow\left(\sqrt{x}+\dfrac{4}{\sqrt{x}}+8\right)\left(\sqrt{x}+\dfrac{4}{\sqrt{x}}-1\right)=36\)
Đặt \(\sqrt{x}+\dfrac{4}{\sqrt{x}}-1=t\ge3\)
\(t\left(t+9\right)=36\Leftrightarrow t^2+9t-36=0\)
\(\Rightarrow\left[{}\begin{matrix}t=3\\t=-12\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{x}+\dfrac{4}{\sqrt{x}}-1=3\)
\(\Leftrightarrow x-4\sqrt{x}+4=0\Leftrightarrow\left(\sqrt{x}-2\right)^2=0\)
\(\Leftrightarrow x=4\)
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![[ ]](https://hoc24.vn/images/avt/avt78337201_256by256.jpg)
giải phương trình :
\(9\left(\sqrt{x+1}+\sqrt{x-2}\right)+1=4\left(\sqrt{\left(x+1\right)^3}-\sqrt{\left(x-2\right)^3}\right)\)
giải pt
\(\frac{2\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)}{\left(1-\sqrt{2}\right)\left(1-\sqrt{3}\right)}+\frac{3\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}-\sqrt{3}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{2}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-2\right)}\)=3x-1
Giải phương trình :
\(\frac{2\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)}{\left(1-\sqrt{2}\right)\left(1-\sqrt{3}\right)}+\frac{3\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}-\sqrt{3}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{2}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{2}\right)}=3x-1\) .
Dùng liên hợp.
pt <=> \(\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)\left(1+\sqrt{2}\right)\left(1+\sqrt{3}\right)\)
\(-3\left(x-1\right)\left(x-\sqrt{3}\right)\left(\sqrt{2}+1\right)\left(\sqrt{2}+\sqrt{3}\right)\)
\(+2\left(x-1\right)\left(x-\sqrt{2}\right)\left(\sqrt{3}+1\right)\left(\sqrt{3}+\sqrt{2}\right)=3x-1\)
<=> \(\left(x-\sqrt{3}\right)\left(1+\sqrt{2}\right)\left[\left(x-\sqrt{2}\right)\left(1+\sqrt{3}\right)-\left(x-1\right)\left(\sqrt{2}+\sqrt{3}\right)\right]\)
\(-2\left(x-1\right)\left(\sqrt{3}+\sqrt{2}\right)\left[\left(x-\sqrt{3}\right)\left(1+\sqrt{2}\right)-\left(x-\sqrt{2}\right)\left(1+\sqrt{3}\right)\right]\)
\(=3x-1\)
<=> \(\left(x-\sqrt{3}\right)\left(1+\sqrt{2}\right)\left(x+\sqrt{3}\right)\left(1-\sqrt{2}\right)\)
\(-2\left(x-1\right)\left(\sqrt{3}+\sqrt{2}\right)\left(x+1\right)\left(\sqrt{2}-\sqrt{3}\right)=3x-1\)
<=> \(3-x^2-2\left(1-x^2\right)=3x-1\)
<=> \(x^2-3x+2=0\) phương trình bậc 2.
Em làm tiếp nhé!
27 tháng 11 2021 lúc 15:51
Giải phương trình:
a) \(5x^2-10x=4\left(x-1\right)\sqrt{x^2-2x+2}\)
b) \(\sqrt{2x^2+22x+29}-x-2=2\sqrt{2x+3}\)
c) \(x^3-7x^2+9x+12=\left(x-3\right)\left(x-2+5\sqrt{x-3}\right)\left(\sqrt{x-3}-1\right)\)
Giải phương trình: \(\sqrt{\left(x^2+1\right)\left(x+3\right)\left(x^4+5\right)\left(x+7\right)}=\sqrt{\left(x+2\right)\left(x^4+4\right)\left(x+6\right)\left(x^2+8\right)}\)