Tìm x, biết: (22 - 1) . ( x-1) = 22 + ( 62 + 26 ) : (56 .2)
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\(B=\frac{1+x^2+x^4+...+x^{26}}{1+x^4+x^8+...+x^{24}}\)
\(=\frac{\frac{\left(x^2-1\right)\left(1+x^2+x^4+...+x^{26}\right)}{x^2-1}}{\frac{\left(x^4-1\right)\left(1+x^4+x^8+...+x^{24}\right)}{x^4-1}}\)
\(=\frac{\frac{x^{28}-1}{x^2-1}}{\frac{x^{28}-1}{x^4-1}}=\frac{x^4-1}{x^2-1}=x^2+1\)
\(2\left(x+56\right)\left(x-6\right)=3^{25}:3^{22}\)
\(\Rightarrow2\left(x+56\right)\left(x-6\right)=3^{25-22}\)
\(\Rightarrow2\left(x+56\right)\left(x-6\right)=3^3\)
\(\Rightarrow\left(x+56\right)\left(x-6\right)=\dfrac{27}{2}\)
\(\Rightarrow x^2-6x+56x-336=\dfrac{27}{2}\)
\(\Rightarrow x^2+50x-336=\dfrac{27}{2}\)
\(\Rightarrow x^2+50x+625-961=\dfrac{27}{2}\)
\(\Rightarrow\left(x+25\right)^2=\dfrac{27}{2}+961\)
\(\Rightarrow\left(x+25\right)^2=\dfrac{1949}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x+25=\sqrt{\dfrac{1949}{2}}\\x+25=-\sqrt{\dfrac{1949}{2}}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{1949}{2}}-25\\x=-\sqrt{\dfrac{1949}{2}}-25\end{matrix}\right.\)