\(ĐK:x\ge5\)

Đặt \(\left\{{}\begin{matrix}\sqrt{x}=a\\\sqrt{x-5}=b\end{matrix}\right.\left(a,b\ge0\right)\Leftrightarrow4b^2-3a^2=x-20\)

\(PT\Leftrightarrow4b^2-3a^2+a+b+ab=0\\ \Leftrightarrow4ab+4b^2-3a^2-3ab+a+b=0\\ \Leftrightarrow4b\left(a+b\right)-3a\left(a+b\right)+\left(a+b\right)=0\\ \Leftrightarrow\left(a+b\right)\left(4b-3a+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}a+b=0\left(\text{loại do }a+b>0\right)\\4b-3a+1=0\left(1\right)\end{matrix}\right.\\ \left(1\right)\Leftrightarrow4\sqrt{x-5}=3\sqrt{x}-1\\ \Leftrightarrow16x-80=9x-6\sqrt{x}+1\\ \Leftrightarrow7x+6\sqrt{x}-81=0\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=3\\\sqrt{x}=-\dfrac{27}{7}\left(loại\right)\end{matrix}\right.\Leftrightarrow x=9\left(nhận\right)\)

=11/2(-1/5+3/7-4/5+4/7)

=11/2(1-1)

=0

\(\left(\dfrac{-1}{5}+\dfrac{3}{7}\right):\dfrac{2}{11}+\left(\dfrac{-4}{5}+\dfrac{4}{7}\right):\dfrac{2}{11}\) 

\(=\dfrac{8}{35}:\dfrac{2}{11}+\dfrac{-8}{35}:\dfrac{2}{11}\) 

\(=\dfrac{2}{11}:\left(\dfrac{8}{35}+\dfrac{-8}{35}\right)\) 

\(=\dfrac{2}{11}:0=0\) 

\(=\dfrac{32}{15}\cdot\dfrac{9}{17}\cdot\dfrac{3}{32}\cdot\dfrac{-17}{3}=-\dfrac{9}{3}=-3\)

=(22/15.3/32)   .   (9/17  :  -3/17)

=66/480     .     (-3)

=11/80  . (-3)

=-33/80

\(\left(2\dfrac{2}{15}\cdot\dfrac{9}{17}\cdot\dfrac{3}{32}\right):\left(-\dfrac{3}{17}\right)\)

\(=\left(\dfrac{32}{15}\cdot\dfrac{9}{17}\cdot\dfrac{3}{32}\right):\left(-\dfrac{3}{17}\right)\)

\(=\dfrac{9}{85}:\left(-\dfrac{3}{17}\right)\)

\(=\dfrac{9}{85}\cdot-\dfrac{17}{3}\)

\(=-\dfrac{3}{5}\)

Đề là vầy đúng không bạn \(5^{n+3}-2^{n+3}+2^{n+1}-5^{n+2}+2^n\)

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

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

\(=5^{n+2}.4-2^n\left(8-2-1\right)\)

\(=5^{n+1}.2.2.5-2^{n-1}.2.5\)

\(=5^{n+1}.2.10-2^{n-1}.10\)

do \(5^{n+1}.2.10\)chia hết cho 10 với mọi n \

\(2^{n-1}.10\)chia hết cho 10 với mọi n

suy ra \(5^{n+1}.2.10-2^{n-1}.10\)chia hết cho 10 với mọi n

suy ra \(5^{n+3}-2^{n+3}+2^{n+1}-5^{n+2}+2^n\)chia hết cho 10 với mọi n

(x-2)³=216

=>\(\left(x-2\right)^3=6^3\)

=>x-2=6

=>x=8

x=8

\(\left(x-2\right)^3=216\\ \Rightarrow\left(x-2\right)^3=6^3\\ \Rightarrow x-2=6\\ \Rightarrow x=8\)

Vậy x = 8