\(\frac{\sqrt{x}-2}{\sqrt{x}+1}=\frac{\sqrt{x}-1}{\sqrt{x}+3}\).Giải PT
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Giải pt: \(\frac{1}{\sqrt{x+3}+\sqrt{x+2}}+\frac{1}{\sqrt{x+2}+\sqrt{x+1}}+\frac{1}{\sqrt{x+1}+\sqrt{x}}=1\)
Giải pt \(\frac{1}{\sqrt{x-1}+\sqrt{x-2}}+\frac{1}{\sqrt{x-2}+\sqrt{x-3}}+...+\frac{1}{\sqrt{x-9}+\sqrt{x-10}}=1\)
Giải pt: \(x+\sqrt[3]{x^3-x^2}+\sqrt[3]{x^3-x}=\sqrt[3]{x^2+x+\frac{1}{3}}+\sqrt[3]{x^2+\frac{1}{3}}+\sqrt[3]{x+\frac{1}{3}}\)
Giải pt \(\frac{1}{\sqrt{x+3}+\sqrt{x+2}}+\frac{1}{\sqrt{x+2}+\sqrt{x+1}}+\frac{1}{\sqrt{x+1}+\sqrt{x}}=1\)
GIÚP MK ĐI!!!!!!!!
olm còn lỗi nên ko trình bày bth đc, bn tự viết lại nhá :))
\(\frac{1}{\sqrt{x+3}+\sqrt{x+2}}=\frac{\sqrt{x+3}-\sqrt{x+2}}{\left(\sqrt{x+3}+\sqrt{x+2}\right)\left(\sqrt{x+3}-\sqrt{x+2}\right)}\)
\(\frac{1}{\sqrt{x+2}+\sqrt{x+1}}=\frac{\sqrt{x+2}-\sqrt{x+1}}{\left(\sqrt{x+2}+\sqrt{x+1}\right)\left(\sqrt{x+2}-\sqrt{x+1}\right)}\)
\(\frac{1}{\sqrt{x+1}+\sqrt{x}}=\frac{\sqrt{x+1}-\sqrt{x}}{\left(\sqrt{x+1}+\sqrt{x}\right)\left(\sqrt{x+1}-\sqrt{x}\right)}\)
\(VT=\sqrt{x+3}-\sqrt{x+2}+\sqrt{x+2}-\sqrt{x+1}+\sqrt{x+1}-\sqrt{x}\)
\(VT=\sqrt{x+3}-\sqrt{x}=1\)
Dễ r -,-
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Giải pt
\(\sqrt{2x+\frac{2013-1}{\sqrt{2-x^2}}}-\sqrt[3]{2014-\frac{2013-1}{\sqrt{2-x^2}}}=\sqrt{x+2013}-\sqrt[3]{x+1}\)
Giải pt :
a) \(x^2+3x\sqrt[3]{3x+3}-12+\frac{1}{\sqrt{x}}=\frac{\sqrt{x}+8}{x}\)
b) \(\sqrt{\left(x-1\right)\left(3-x\right)}+\sqrt{x+2}=\sqrt{x-1}+\sqrt{3-x}+\frac{x}{2}\)
giải pt \(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}x+\frac{2}{\sqrt{7}-\sqrt{5}}=\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}x\)
Nhân liên hợp rồi rút gọn thì ta sẽ ra. Tôi nghĩ vậy
Giải pt: \(\frac{\sqrt{x+1}}{\sqrt{x+1}-\sqrt{3-x}}=x-\frac{1}{2}\)
Giải pt sau:
\(A=\left(\frac{\sqrt{3}}{x^2+x\sqrt{3}+3}+\frac{3}{x^3-\sqrt{27}}\right)\left(\frac{x}{\sqrt{3}}+\frac{\sqrt{3}}{x}+1\right)\)
\(A=\left(\frac{\sqrt{3}}{x^2+x\sqrt{x}+3}+\frac{3}{x^3-\sqrt{27}}\right)\left(\frac{x}{\sqrt{3}}+\frac{\sqrt{3}}{x}+1\right)\)
\(\Leftrightarrow A=\left[\frac{\sqrt{3}\left(x-\sqrt{3}\right)}{\left(x-\sqrt{3}\right)\left(x^2+x\sqrt{3}+3\right)}+\frac{3}{\left(x-\sqrt{3}\right)\left(x+x\sqrt{3}+3\right)}\right]\left(\frac{x^2+3+x\sqrt{3}}{x\sqrt{3}}\right)\)
\(\Leftrightarrow A=\frac{x\sqrt{3}-3+3}{\left(x-\sqrt{3}\right)\left(x^2+x\sqrt{3}+3\right)}.\frac{x^2+x\sqrt{3}+3}{x\sqrt{3}}\)
\(\Leftrightarrow A=\frac{1}{x-\sqrt{3}}\)
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giải pt \(\sqrt{2x+\frac{2013x-1}{\sqrt{2-x^2}}}-\sqrt[3]{2014-\frac{2013x-1}{\sqrt{2-x^2}}}=\sqrt{x+2003}-\sqrt[3]{x+1}\)
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