Giải PT: \(x^2+\left(3-\sqrt{x^2+2}\right)x=1+2\sqrt{x^2+2}\)
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18 tháng 6 2021 lúc 21:19
Giải pt:
\(x^3+\left(x+1\right)\sqrt{x+1}+2\sqrt{2}=\left(x+\sqrt{x+1}+\sqrt{2}\right)^3\)
Đk:\(x\ge-1\)
Đặt \(\left(a,b,c\right)=\left(x;\sqrt{x+1};\sqrt{2}\right)\)
Pt tt: \(a^3+b^3+c^3=\left(a+b+c\right)^3\)
\(\Leftrightarrow a^3+b^3+c^3=\left(a+b\right)^3+3\left(a+b\right)^2c+3\left(a+b\right)c^2+c^3\)
\(\Leftrightarrow0=3ab\left(a+b\right)+3\left(a+b\right)^2c+3\left(a+b\right)c^2\)
\(\Leftrightarrow3\left(a+b\right)\left(ab+ac+bc+c^2\right)=0\)
\(\Leftrightarrow3\left(a+b\right)\left(b+c\right)\left(a+c\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a+b=0\\b+c=0\\a+c=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x+\sqrt{x+1}=0\\\sqrt{x+1}+\sqrt{2}=0\left(vn\right)\\x+\sqrt{2}=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}\sqrt{x+1}=-x\\x=-\sqrt{2}\left(ktm\right)\end{matrix}\right.\)\(\Rightarrow\)\(\sqrt{x+1}=-x\)
\(\Leftrightarrow\left\{{}\begin{matrix}-1\le x\le0\\x+1=x^2\end{matrix}\right.\)\(\Rightarrow x=\dfrac{1-\sqrt{5}}{2}\) (tm)
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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 pt \(x^2+\left(3-x\right)\sqrt{2x-1}=x\left(3\sqrt{2x^2-5x+2}-\sqrt{x-2}\right)\)
Giải PT: \(\left(\sqrt{x+2}-\sqrt{x-2}\right).\left(1+\sqrt{x^2+7x+10}\right)=3\)
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, \(\sqrt[3]{2-x}=1-\sqrt{x-1}\)
b, \(2\sqrt[3]{3x-2}+3\sqrt{6-5x}-8=0\)
c, \(\left(x+3\right)\sqrt{-x^2-8x+48}=x-24\)
d, \(\sqrt[3]{\left(2-x\right)^2}+\sqrt[3]{\left(7+x\right)\left(2-x\right)}=3\)
e, \(\dfrac{\sqrt[3]{7-x}-\sqrt[3]{x-5}}{\sqrt[3]{7-x}+\sqrt[3]{x-5}}=6-x\)
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, bất pt
a) \(\left(\sqrt{x+3}-\sqrt{x+1}\right)\left(x^2+\sqrt{x^2+4x+3}=2x\right)\)
b) \(\left(x^2-3x+2\right)\left(x^2-12x+32\right)\le4x^2\)
c) \(2\sqrt{3x+7}-5\sqrt[3]{x-6}=4\)
Giải pt: \(\sqrt{1+\sqrt{1-x^2}}=\left[\left(\sqrt{1+x}\right)^3-\left(\sqrt{1-x}\right)^3\right]=2+\sqrt{1-x^2}\)
Xem thêm câu trả lời
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, \(\sqrt{x-2}-\sqrt{x+2}=2\sqrt{x^2-4}-2x+2\)