ĐKXĐ; \(x\ge-1\)

Đặt \(\sqrt[3]{x-2}=t\left(t\ge-\sqrt[3]{3}\right)\Rightarrow x+1=t^3+3\)

Phương trình trở thành:

\(t+\sqrt{t^3+2}=3\Leftrightarrow\sqrt{t^3+2}=3-t\)

\(\Leftrightarrow\left\{{}\begin{matrix}t^3+3=9-6t+t^2\\3-t\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}t^3-t^2+6t-6=0\\-\sqrt[3]{3}\le t\le3\end{matrix}\right.\)

\(\Leftrightarrow\left(t-1\right)\left(t^2+6\right)=0\Leftrightarrow t=1\) (thoả đk)

=> x = 3 (thoả)

Kết luận nhiệm pt: \(S=\left\{3\right\}\)

a/ \(\left(\frac{3}{\sqrt{5}-\sqrt{2}}+\frac{4}{\sqrt{6}+\sqrt{2}}\right)\left(\sqrt{3-1}\right)^2\)

\(=\left(\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{5}+\sqrt{2}\right)\left(\sqrt{5}-\sqrt{2}\right)}+\frac{4\left(\sqrt{6}-\sqrt{2}\right)}{\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}\right)\left(\sqrt{3}-1\right)^2\)

\(\)\(=\left(\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{3}+\frac{4\left(\sqrt{6}-\sqrt{2}\right)}{4}\right)\left(\sqrt{3}-1\right)^2\)

\(=\left(\sqrt{5}+\sqrt{2}+\sqrt{6}-\sqrt{2}\right)\left(\sqrt{3}-1\right)^2=\left(\sqrt{5}+\sqrt{6}\right)\left(\sqrt{3}-1\right)^2\)

b/ \(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{99}+\sqrt{100}}\)

\(=\frac{\sqrt{2}-1}{\left(1+\sqrt{2}\right)\left(\sqrt{2}-1\right)}+\frac{\sqrt{3}-\sqrt{2}}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}+...+\frac{\sqrt{100}-\sqrt{99}}{\left(\sqrt{99}+\sqrt{100}\right)\left(\sqrt{100}-\sqrt{99}\right)}\)

\(=\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+...+\sqrt{100}-\sqrt{99}\)

\(=\sqrt{100}-1\)

Ta có: \(A=\left(5+\frac{7-\sqrt{21}}{\sqrt{7}-\sqrt{3}}\right)\sqrt{16-5\sqrt{7}}\)

\(=\left(5+\frac{\sqrt{7}\left(\sqrt{7}-\sqrt{3}\right)}{\sqrt{7}-\sqrt{3}}\right)\sqrt{16-5\sqrt{7}}\)

\(=\left(5+\sqrt{7}\right)\sqrt{16-5\sqrt{7}}\)

\(\Rightarrow\sqrt{2}A=\left(5+\sqrt{7}\right)\sqrt{32-10\sqrt{7}}\)

\(=\left(5+\sqrt{7}\right)\sqrt{\left(5-\sqrt{7}\right)^2}=\left(5+\sqrt{7}\right)\left(5-\sqrt{7}\right)\)

\(=25-7=18\)

Vậy \(A=\frac{18}{\sqrt{2}}=9\sqrt{2}\)

2/3>x>-2/3

(x-34).15=0                 x-34=0                      x=34

\(5+7+0+12=24\)

nhé bạn

đáp án là123655 nha bn

k nha

3 số đó là:721;631;532

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