`(5^{x})^{2}=125^{3}:5^{2}`

`5^{2x}=(5^{2})^{3}:5^{2}`

`5^{2x}=5^{6}:5^{2}`

`5^{2x}=5^{4}`

`2x=4`

`x=4:2=2`

\(D=\dfrac{1}{1 \times 3}+\dfrac{1}{3 \times 5}+\dfrac{1}{5 \times 7}+...+\dfrac{1}{2007 \times 2009}+\dfrac{1}{2009 \times 2011}\)

\(D=\dfrac{1}{2} \times (\dfrac{2}{1 \times 3}+\dfrac{2}{3 \times 5}+\dfrac{2}{5 \times 7}+...+\dfrac{2}{2007 \times 2009}+\dfrac{2}{2009 \times 2011})\)

\(D=\dfrac{1}{2} \times (1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2009}-\dfrac{1}{2011})\)

\(D=\dfrac{1}{2} \times (1-\dfrac{1}{2011})\)

\(D=\dfrac{1}{2} \times \dfrac{2010}{2011}\)

\(D=\dfrac{1005}{2011}\)

\(D=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+.....+\dfrac{1}{2007.2009}+\dfrac{1}{2009.2011}\)

`=>` \(D=\dfrac{1}{2}.\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+....+\dfrac{1}{2007.2009}+\dfrac{1}{2009.2011}\right)\)

\(D=\dfrac{1}{2}.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2009}-\dfrac{1}{2011}\right)\)

`C=1/2 . (1-1/2011)`

`C=1/2 . (2011/2011- 1/101)`

`C=1/2 . 2010/2011`

`C=1005/2011`

a, \(x^8-3x^4+3x^2-1-x^8+1=0\Leftrightarrow-3x^2\left(x^2-1\right)=0\Leftrightarrow x=0;x=1;x=-1\)

b, \(x^3-6x^2+12x-8-x^3+27+6x^2+12x+6=49\)

\(\Leftrightarrow24x-24=0\Leftrightarrow x=1\)

c, \(8x^3-27-98=0\Leftrightarrow8x^3-125=0\Leftrightarrow\left(2x-5\right)\left(4x^2+10x+25\ne0\right)=0\Leftrightarrow x=\dfrac{5}{2}\)

d, \(27-\dfrac{1}{8}x^3-19=0\Leftrightarrow8-\dfrac{1}{8}x^3=0\Leftrightarrow\left(2-\dfrac{1}{2}x\right)\left(4+x+\dfrac{1}{4}x^2\ne0\right)=0\Leftrightarrow x=4\)

\(C=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+.......+\dfrac{1}{99.101}\)

`=>` \(C=\dfrac{1}{2}.\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+.....+\dfrac{1}{99.101}\right)\)

\(C=\dfrac{1}{2}.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+.....+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

`C=1/2 . (1-1/101)`

`C=1/2 . (101/101- 1/101)`

`C=1/2 . 100/101`

`C=50/101`

\(C=\dfrac{1}{1 \times 3}+\dfrac{1}{3 \times 5}+\dfrac{1}{5 \times 7}+...+\dfrac{1}{99 \times 101}\)

\(C=\dfrac{1}{2} \times (\dfrac{2}{1 \times 3}+\dfrac{2}{3 \times 5}+\dfrac{2}{5 \times 7}+...+\dfrac{2}{99 \times 101})\)

\(C=\dfrac{1}{2} \times (1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101})\)

\(C=\dfrac{1}{2} \times (1-\dfrac{1}{101})\)

\(C=\dfrac{1}{2} \times \dfrac{100}{101}\)

\(C=\dfrac{50}{101}\)

 y-2/3-2/15-2/35-2/63=1/9

= y - 2/3 = 1/9 +2/63+2/35+2/15

= y - 2/3 = 1/3

= y = 1/3 + 2/3

= y = 3/3 

= y = 1

`y - 2/3 - 2/15 - 2/35 - 2/63 = 1/9`

`=>` \(y-\dfrac{2}{1.3}-\dfrac{2}{3.5}-\dfrac{2}{5.7}-\dfrac{2}{7.9}=\dfrac{1}{9}\)

`=> y - 1-1/3+1/3-1/5+1/5-1/7+1/7-1/9=1/9`

`y-1-1/9=1/9`

`y-9/9-1/9=1/9`

`y-8/9=1/9`

`y=1/9+8/9`

`y = 9/9`

`=>y = 1`

`(5215 + 4325 + 4785 + 5675) : (5 xx 2 xx 2 : 5)`

`=(5215 + 4325 + 4785 + 5675) : (10 xx 2 : 5)`

`=(5215 + 4325 + 4785 + 5675) : ( 20 : 4)`

`=(5215 + 4325 + 4785 + 5675) : 4`

`=(9540+ 4785 + 5675) : 4`

`=(14325+5675):4`

`=20000:4`

`=5000`

pls~pls~pls