\(2x\left(x-5\right)-x\left(x-10\right)+1=26\)

\(2x^2-10x-x^2+10x-25=0\)

\(x^2-25=0\)

\(\left(x-5\right)\left(x+5\right)=0\)

\(\left[{}\begin{matrix}x=5\\x=-5\end{matrix}\right.\)

\(7\left(2x-5\right)-5\left(7x-2\right)+2\left(5x+7\right)=\left(x-2\right)-\left(x+4\right)\)

\(14x-35-35x+10+10x+14=-6\)

\(-11x-11=-6\)

\(x=-\dfrac{5}{11}\)

\(10x-5-32+12x=7\)

\(22x=44\)

\(x=2\)

 

 

 

\(\left(a+b+c\right)^2=3\left(ab+bc+ca\right)\)

\(a^2+b^2+c^2+2ab+2bc+2ca=3ab+3bc+3ca\)

\(a^2+b^2+c^2=ab+bc+ca\)

\(\dfrac{1}{2}\left(2a^2+2b^2+2c^2-2ab-2bc-2ca\right)=0\)

\(\left(a^2-2ab+b^2\right)+\left(b^2-2bc+c^2\right)+\left(c^2-2ac+a^2\right)=0\)

\(\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2=0\)

\(\left\{{}\begin{matrix}a-b=0\\b-c=0\\c-a=0\end{matrix}\right.\)

\(< =>a=b=c\)

 

 

\(E=1.2+2.3+3.4+...+2020.2021\)

\(3E=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+....+2020.2021.\left(2022-2019\right)\)

\(3E=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+2020.2021.2022-2019.2020.2021\)

\(3E=2020.2021.2022\)

\(E=2020.2021.674\)

\(ĐKXĐ:x\ge3\)

\(\sqrt{x-3+4\sqrt{x-3}+4}+\sqrt{x-3-4\sqrt{x-3}+4}=x-11\)

\(\sqrt{\left(\sqrt{x-3}+2\right)^2}+\sqrt{\left(\sqrt{x-3}-2\right)^2}=x-11\)

\(\sqrt{x-3}+2+\sqrt{x-3}-2=x-11\)

\(2\sqrt{x-3}=x-11\)

\(4\left(x-3\right)=\left(x-11\right)^2\)

\(4x-12=x^2-22x+121\)

\(x^2-26x+133=0\)

\(\left(x-19\right)\left(x-7\right)=0\)

\(\left[{}\begin{matrix}x=19\left(TM\right)\\x=7\left(TM\right)\end{matrix}\right.\)

\(a,ĐKXĐ:x\ge\dfrac{3}{2}\)

\(\sqrt{2x-3}=2\sqrt{x}-2\)

\(2x-3=4x-8\sqrt{x}+4\)

\(2x-8\sqrt{x}+7=0\)

\(\sqrt{\Delta}=\sqrt{\left(-8\right)^2-4.2.7}=2\sqrt{2}\)

\(x_1=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{4+\sqrt{2}}{2}\left(TM\right)\)

\(x_2=\dfrac{4-\sqrt{2}}{2}\left(KTM\right)\)

\(b,\sqrt{\dfrac{4x+3}{\sqrt{x+1}}}=3\)

\(ĐKXĐ:x\ge-\dfrac{3}{4}\)

\(\dfrac{4x+3}{\sqrt{x+1}}=9\)

\(\left(4x+3\right)^2=81x+81\)

\(16x^2+24x+9=81x+81\)

\(16x^2-57x-72=0\)

\(\sqrt{\Delta}=9\sqrt{97}\)

\(x_1=\dfrac{57+9\sqrt{97}}{32}\left(TM\right)\)

\(x_2=\dfrac{57-9\sqrt{97}}{32}\left(KTM\right)\)

\(c,ĐKXĐ:x>1\)

\(\dfrac{\sqrt{x^2+3x-x-3}}{\sqrt{x-1}}=x+3\)

\(\dfrac{\sqrt{\left(x-1\right)\left(x+3\right)}}{\sqrt{x-1}}=x+3\)

\(\sqrt{x+3}=x+3\)

\(x+3=x^2+6x+9\)

\(x^2+5x+6=0\)

\(\left(x+3\right)\left(x+2\right)=0\)

\(\left[{}\begin{matrix}x=-3\left(KTM\right)\\x=-2\left(KTM\right)\end{matrix}\right.\)

\(d,x>3\)

\(\dfrac{\sqrt{x^2-4x+3}}{\sqrt{x-3}}=x-1\)

\(\dfrac{\sqrt{x-3}\sqrt{x-1}}{\sqrt{x-3}}=x-1\)

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

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

\(x=2\left(KTM\right)\)

 

 

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