\(c)\)\(\dfrac{\sqrt{x}-2}{\sqrt{x}-5}=\dfrac{\sqrt{x}-4}{\sqrt{x}-6}\left(ĐK:x>=0;x\ne\left\{25;36\right\}\right)\\ < =>\left(\sqrt{x}-2\right)\left(\sqrt{x}-6\right)=\left(\sqrt{x}-5\right)\left(\sqrt{x}-4\right)\\ < =>x-8\sqrt{x}+12=x-9\sqrt{x}+20\\ < =>x-x+9\sqrt{x}-8\sqrt{x}=20-12\\ < =>\sqrt{x}=8\\ < =>x=64\left(TMDK\right)=>S=\left\{64\right\}\)

\(d)\)\(\sqrt{4x-8}-\dfrac{1}{2}\sqrt{x-2}+\sqrt{9x-18}=9\left(ĐK:x>=2\right)\\ < =>\sqrt{4}.\sqrt{x-2}-\dfrac{1}{2}\sqrt{x-2}+\sqrt{9}.\sqrt{x-2}=9\\ < =>\sqrt{x-2}.\left(\sqrt{4}-\dfrac{1}{2}+\sqrt{9}\right)=9\\ < =>\sqrt{x-2}.\dfrac{9}{2}=9\\ < =>\sqrt{x-2}=2\\ < =>x-2=4\\ < =>x=6\left(TMDK\right)=>S=\left\{6\right\}\)

\(a)\)\(\sqrt{x-5}+2\sqrt{25x-125}=22\left(ĐK:x>=5\right)\\ < =>\sqrt{x-5}+2.\sqrt{25}.\sqrt{x-5}=22\\ < =>\sqrt{x-5}.\left(1+2\sqrt{25}\right)=22\\ < =>\sqrt{x-5}.11=22\\ < =>\sqrt{x-5}=2\\ < =>x-5=4\\ < =>x=9\left(TMDK\right)=>S=\left\{9\right\}\)

\(b)\)\(\sqrt{18x+9}-\sqrt{8x+4}+\dfrac{1}{3}\sqrt{2x+1}=4\left(ĐK:x>=-\dfrac{1}{2}\right)\\ < =>\sqrt{9}.\sqrt{2x+1}-\sqrt{4}.\sqrt{2x+1}+\dfrac{1}{3}\sqrt{2x+1}=4\\ < =>\sqrt{2x+1}.\left(\sqrt{9}-\sqrt{4}+\dfrac{1}{3}\right)=4\\ < =>\sqrt{2x+1}.\dfrac{4}{3}=4\\ < =>\sqrt{2x+1}=3\\ < =>2x+1=9\\ < =>x=4\left(TMDK\right)=>S=\left\{4\right\}\)

\(16x^3y+0,25yz^3=\dfrac{1}{4}y\left(64x^3+z^3\right)\\ =\dfrac{1}{4}y\left[\left(4x\right)^3+z^3\right]\\ =\dfrac{1}{4}y\left(4x+z\right)\left(16x^2-4xz+z^2\right)\)

\(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+2019\right)+2019=2019\\ =>\left(x+x+x+...+x\right)+\left(1+2+...+2019\right)=0\\ =>2020x+\dfrac{\left(2019+1\right).2019}{2}=0\\ =>2020x+\dfrac{2020.2019}{2}=0\\ =>2020.\left(x+\dfrac{2019}{2}\right)=0\\ =>x+\dfrac{2019}{2}=0\\ =>x=-\dfrac{2019}{2}\left(KTM\right)\)

\(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+20\right)=20\\ =>\left(x+x+x+...+x\right)+\left(1+2+...+20\right)=20\\ =>21x+\dfrac{\left(20+1\right).20}{2}=20\\ =>21x+21.10=20\\ =>21x=-190\\ =>x=-\dfrac{190}{21}\)

\(Mà : x\in Z\)

\(=>x\in\varnothing\)

\(\dfrac{1}{1x2}+\dfrac{2}{2x4}+\dfrac{3}{4x7}+\dfrac{4}{7x11}+...+\dfrac{10}{46x56}\\ =\dfrac{2}{1x2}-\dfrac{1}{1x2}+\dfrac{4}{2x4}-\dfrac{2}{2x4}+\dfrac{7}{4x7}-\dfrac{4}{4x7}+\dfrac{11}{7x11}-\dfrac{7}{7x11}+...+\dfrac{56}{46x56}-\dfrac{46}{46x56}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{46}-\dfrac{1}{56}\\ =1-\dfrac{1}{56}=\dfrac{55}{56}\)

\(124x16+16x76=16x\left(124+76\right)=16x200=3200\\ 96,28x3,527+3,527x3,72=3,527x\left(96,28+3,72\right)=3,527x100=352,7\\ \dfrac{5}{8}x\dfrac{1}{9}+\dfrac{3}{8}x\dfrac{1}{9}=\dfrac{1}{9}x\left(\dfrac{5}{8}+\dfrac{3}{8}\right)=\dfrac{1}{9}x\dfrac{8}{8}=\dfrac{1}{9}x1=\dfrac{1}{9}\)

\(\left(3x-2\right)^3=\left(3x\right)^3-3.\left(3x\right)^2.2+3.3x.2^2-2^3\\ =27x^3-54x^2+36x-8\)

\(100+102+104+...+1000\)

\(Số\ số\ hạng\ dãy\ trên : (1000-100):2+1=451(số\ hạng)\)

\(Tổng\ dãy\ trên : (1000+100).451:2=248050\)

\(x^3+8y^3=x^3+\left(2y\right)^3=\left(x+2y\right)\left[x^2-x.2y+\left(2y\right)^2\right]=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)\(a^6-b^3=\left(a^2\right)^3-b^3=\left(a^2-b\right)\left[\left(a^2\right)^2+a^2.b+b^2\right]=\left(a^2-b\right)\left(a^4+a^2b+b^2\right)\)