Giải PT\(\left(2+\sqrt{x-4}\right)\left(\sqrt{x-4}+2\right)=2x\)
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giải pt :
a, \(\left(2x-6\right)\sqrt{x+4}-\left(x-5\right)\sqrt{2x+3}=3\left(x-1\right)\)
b, \(\left(4x+1\right)\sqrt{x+2}-\left(4x-1\right)\sqrt{x-2}=21\)
c, \(\left(4x+2\right)\sqrt{x+1}-\left(4x-2\right)\sqrt{x-1}=9\)
d, \(\left(2x-4\right)\sqrt{3x-2}+\sqrt{x+3}=5x-7+\sqrt{3x^2+7x-6}\)
giải các PT sau :a) left|2x+3right|-left|xright|+left|x-1right|2x+4b) sqrt{x}-dfrac{4}{sqrt{x+2}}+sqrt{x+2}0c) sqrt{x+sqrt{2x-1}}+sqrt{x-sqrt{2x-1}}sqrt{2}d) x+sqrt{x+dfrac{1}{2}+sqrt{x+dfrac{1}{4}}}4e) sqrt{4x+3}+sqrt{2x+1}6x+sqrt{8x^2+10x+3}-16f)sqrt[3]{x-2}+sqrt{x+1}3GIÚP MÌNH VỚI MÌNH ĐANG CẦN GẤP
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giải các PT sau :
a) \(\left|2x+3\right|-\left|x\right|+\left|x-1\right|=2x+4\)
b) \(\sqrt{x}-\dfrac{4}{\sqrt{x+2}}+\sqrt{x+2}=0\)
c) \(\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=\sqrt{2}\)
d) \(x+\sqrt{x+\dfrac{1}{2}+\sqrt{x+\dfrac{1}{4}}}=4\)
e) \(\sqrt{4x+3}+\sqrt{2x+1}=6x+\sqrt{8x^2+10x+3}-16\)
f)\(\sqrt[3]{x-2}+\sqrt{x+1}=3\)
GIÚP MÌNH VỚI MÌNH ĐANG CẦN GẤP
giải pt :a,\(\left(2x+6\right)\sqrt{x+4}-\left(x-5\right)\sqrt{2x+3}=3\left(x-1\right)\)
b, \(\left(4x+1\right)\sqrt{x+2}-\left(4x-1\right)\sqrt{x-2}=21\)
c, \(\left(4x+2\right)\sqrt{x+1}-\left(4x-2\right)\sqrt{x-1}=9\)
d, \(\left(2x-4\right)\sqrt{3x-2}+\sqrt{x+3}=5x-7+\sqrt{3x^2+7x-6}\)
giải pt :
a,\(\left(6x-5\right)\sqrt{x+1}-\left(6x+2\right)\sqrt{x-1}+4\sqrt{x^2-1}=4x-3\)
b, \(\left(9x-2\right)\sqrt{3x-1}+\left(10-9x\right)\sqrt{3-3x}-4\sqrt{-9x^2+12x-3}=4\)
c, \(\left(13-4x\right)\sqrt{2x-3}+\left(4x-3\right)\sqrt{5-2x}=2+8\sqrt{-4x^2+16x-15}\)
3 tháng 11 2021 lúc 22:42
Giải PT: \(\sqrt{\left(x^2+2x\right)^2+4\left(x+1\right)^2}-\sqrt{x^2+\left(x+1\right)^2+\left(x^2+x\right)^2}=2019\)
Chú ý:
\(\left(x^2+2x\right)^2+4\left(x+1\right)^2=\left(x^2+2x\right)^2+4\left(x^2+2x+1\right)=\left(x^2+2x\right)^2+4\left(x^2+2x\right)+4\)
\(=\left(x^2+2x+2\right)^2\)
\(x^2+\left(x+1\right)^2+\left(x^2+x\right)^2\)
\(=\left(x^2+x\right)+x^2+x^2+2x+1\)
\(=\left(x^2+x\right)^2+2x^2+2x+1\)
\(=\left(x^2+x\right)^2+2\left(x^2+x\right)+1\)
\(=\left(x^2+x+1\right)^2\)
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giải pt :
a, \(\left(x^2+2\right)^2+4\left(x+1\right)^3+\sqrt{x^2+2x+5}=\left(2x-1\right)^2+2\)
b, \(\sqrt{4x^2+x+6}=4x-2+7\sqrt{x+1}\)
c, \(\sqrt{x-2}-\sqrt{x+2}=2\sqrt{x^2-4}-2x+2\)
Giải PT: \(\sqrt{x-1}+\sqrt{x+3}+2\sqrt{\left(x-1\right).\left(x^2-3x+5\right)}=4-2x\)
giải pt :
a, \(\sqrt{x-\sqrt{x^2-1}}+\sqrt{x+\sqrt{x^2-1}}=2\)
b, \(\left(x^2+2\right)^2+4\left(x+1\right)^3+\sqrt{x^2+2x+5}=\left(2x-1\right)^2+2\)
c, \(\sqrt{4x^2+x+6}=4x-2+7\sqrt{x+1}\)
d, \(\sqrt{x-2}-\sqrt{x+2}=2\sqrt{x^2-4}-2x+2\)
giải pt \(\left(\sqrt{x+4}-2\right)\left(\sqrt{4-x}+2\right)=2x\)
ĐKXĐ : \(\hept{\begin{cases}x+4\ge0\\4-x\ge0\end{cases}\Leftrightarrow\hept{\begin{cases}x\ge-4\\x\le4\end{cases}\Leftrightarrow}-4\le x\le4}\)
Ta có :\(\left(\sqrt{x+4}-2\right)\left(\sqrt{4-x}+2\right)=2x\)
\(\Leftrightarrow\frac{\left(\sqrt{x+4}-2\right)\left(\sqrt{x+4}+2\right)}{\sqrt{x+4}+2}.\frac{\left(\sqrt{4-x}+2\right)\left(\sqrt{4-x}-2\right)}{\sqrt{4-x}-2}=2x\)
\(\Leftrightarrow\frac{x+4-4}{\sqrt{x+4}+2}.\frac{4-x-4}{\sqrt{4-x}-2}=2x\)
\(\Leftrightarrow\frac{x.\left(-x\right)}{\left(\sqrt{x+4}+2\right)\left(\sqrt{4-x}-2\right)}-2x=0\)
\(\Leftrightarrow x\left[\frac{-x}{\left(\sqrt{x+4}+2\right)\left(\sqrt{4-x}-2\right)}-2\right]=0\)
\(\Leftrightarrow x\left[\frac{x}{\left(\sqrt{x+4}+2\right)\left(\sqrt{4-x}-2\right)}+2\right]=0\)
Tự làm nốt
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