b) \(\dfrac{1}{4-3\sqrt{2}}-\dfrac{1}{4+3\sqrt{2}}=\dfrac{4+3\sqrt{2}-4+3\sqrt{2}}{\left(4-3\sqrt{2}\right)\left(4+3\sqrt{2}\right)}=\dfrac{6\sqrt{2}}{-2}=-3\sqrt{2}\)

c) \(\left(\dfrac{\sqrt{7}+3}{\sqrt{7}-3}-\dfrac{\sqrt{7}-3}{\sqrt{7}+3}\right):\sqrt{28}=\dfrac{\left(\sqrt{7}+3\right)^2-\left(\sqrt{7}-3\right)^2}{\left(\sqrt{7}-3\right)\left(\sqrt{7}+3\right)}:\sqrt{28}=\dfrac{16+6\sqrt{7}-16+6\sqrt{7}}{7-9}=\dfrac{12\sqrt{7}}{-2}=-6\sqrt{7}\)

a) \(36x^2-49=0\Rightarrow\left(6x-7\right)\left(6x+7\right)=0\Rightarrow\left[{}\begin{matrix}6x-7=0\\6x+7=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{6}\\x=-\dfrac{7}{6}\end{matrix}\right.\)

c) \(\left(\dfrac{1}{x}-5\right)\left(\dfrac{1}{x}+5\right)=\dfrac{1}{x^2}-25\)

c) \(\left(x-\dfrac{3}{2}\right)\left(x+\dfrac{3}{2}\right)=x^2-\dfrac{9}{4}\)

c) \(\left(\dfrac{x}{3}-\dfrac{y}{4}\right)\left(\dfrac{x}{3}+\dfrac{y}{4}\right)=\dfrac{x^2}{9}-\dfrac{y^2}{16}\)

c) \(\left(\dfrac{x}{y}-\dfrac{2}{3}\right)\left(\dfrac{x}{y}+\dfrac{2}{3}\right)=\dfrac{x^2}{y^2}-\dfrac{4}{9}\)

c) \(\left(\dfrac{x}{2}+\dfrac{y}{3}\right)\left(\dfrac{y}{3}-\dfrac{x}{2}\right)=\dfrac{y^2}{9}-\dfrac{x^2}{4}\)

c) \(\left(2x-\dfrac{2}{3}\right)\left(\dfrac{2}{3}+2x\right)=4x^2-\dfrac{4}{9}\)

c) \(\left(2x+\dfrac{3}{5}\right)\left(\dfrac{3}{5}-2x\right)=\dfrac{9}{25}-4x^2\)

c) \(\left(\dfrac{1}{2}x-\dfrac{4}{3}\right)\left(\dfrac{4}{4}+\dfrac{1}{2}x\right)=\dfrac{1}{4}x^2-\dfrac{16}{9}\)

c) \(\left(\dfrac{2}{3}x^2-\dfrac{y}{2}\right)\left(\dfrac{2}{3}x^2+\dfrac{y}{2}\right)=\dfrac{4}{9}x^4-\dfrac{y^2}{4}\)

c) \(\left(x^2-y^2\right)^2=x^4-2x^2y^2+y^4\)

c) \(\left(x^2+3^2\right)^2=x^4+18x+81\)

c) \(\left(2x^2+1\right)^2=4x^4+4x^2+1\)

c) \(\left(3x-y^2\right)^2=9x^2-6xy^2+y^4\)

c) \(\left(x+2y^2\right)^2=x^2+4xy^2+4y^4\)

c) \(\left(3x\right)^2-y^2=\left(3x-y\right)\left(3x+y\right)\)

c) \(\left(2x+3y^2\right)^2=4x^2+12xy^2+9y^4\)

c) \(\left(4x-2y^2\right)^2=16x^2-16xy^2+4y^4\)

c) \(\left(4x^2-2y\right)^2=16x^4-16x^2y+4y^2\)

Câu 5: -0,1

Câu 6: Ba số đó là 25,27,29

a) \(x^2+10x+25=0\Rightarrow\left(x+5\right)^2=0\Rightarrow x+5=0\Rightarrow x=-5\)

b) \(x^2+\dfrac{2}{5}x+\dfrac{1}{25}=\dfrac{4}{25}\Rightarrow\left(x+\dfrac{1}{5}\right)^2=\dfrac{4}{25}\Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{5}=\dfrac{2}{5}\\x+\dfrac{1}{5}=-\dfrac{2}{5}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{5}\\x=-\dfrac{3}{5}\end{matrix}\right.\)

d) \(x^2-49=0\Rightarrow\left(x-7\right)\left(x+7\right)=0\Rightarrow\left[{}\begin{matrix}x=7\\x=-7\end{matrix}\right.\)

e) \(16x^2-1=0\Rightarrow\left(4x-1\right)\left(4x+1\right)=0\Rightarrow\left[{}\begin{matrix}4x-1=0\\4x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=-\dfrac{1}{4}\end{matrix}\right.\)

a) \(x^4+81+18x^2=\left(x^2+9\right)^2\)               b)\(\left(3y-4x\right)^2=9y^2-24xy+16x^2\)

a) \(x^2+4y^4-4xy^2=\left(x-2y^2\right)^2\)           b)\(\left(2x-3y\right)^2=4x^2-12xy+9y^2\)

a) \(x^2+10xy+25y^2=\left(x+5y\right)^2\)           b) \(\left(2x-5y\right)^2=4x^2-20xy+25y^2\)

a) \(9y^2-24xy+16x^2=\left(3y-4x\right)^2\)       b) \(\left(2x+3y\right)^2=4x^2+12xy+9y^2\)

a) \(16x^2+9y^4+24xy^2=\left(4x+3y^2\right)^2\)   b) \(\left(3x-5y\right)^2=9x^2-30xy+25y^2\)

a) \(4x^4-4x^2+1=\left(2x^2-1\right)^2\)        b) \(\left(x+2y\right)^2=x^2+4xy+4y^2\)

a) \(36+x^2-12x=\left(x-6\right)^2\)            b)\(\left(x+5y\right)^2=x^2+10xy+25y^2\)

a) \(4x^2-12x+9=\left(2x-3\right)^2\)          b) \(\left(x-2y\right)^2=x^2-4xy+4y^2\)

a) \(1-10x+25x^2=\left(1-5x\right)^2\)        b) \(\left(3x+5y\right)^2=9x^2+30xy+25y^2\)

a) \(6x^3-9x^2=3x^2\left(2x-3\right)\)

b) \(20x^2y-12x^3=4x^2\left(5y-3x\right)\)

Đáp số: \(x^6-64\)