a)

\(\dfrac{1}{2\sqrt{a}-2}-\dfrac{1}{2\sqrt{a}+2}+\dfrac{\sqrt{a}}{1-a}\left(a\ge0;a\ne1\right)\\ =\dfrac{1}{2\left(\sqrt{a}-1\right)}-\dfrac{1}{2\left(\sqrt{a}+1\right)}-\dfrac{\sqrt{a}}{a-1}\\ =\dfrac{\sqrt{a}+1}{2\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}-\dfrac{\sqrt{a}-1}{2\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}-\dfrac{2\sqrt{a}}{2\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\)

\(=\dfrac{\sqrt{a}+1-\sqrt{a}+1-2\sqrt{a}}{2\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\\ =\dfrac{2-2\sqrt{a}}{2\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\\ =\dfrac{-2\left(-1+\sqrt{a}\right)}{2\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\\ =\dfrac{-1}{\sqrt{a}+1}\)

b)

\(\left|A\right|=\dfrac{1}{2}< =>\left[{}\begin{matrix}A=\dfrac{1}{2}\\A=-\dfrac{1}{2}\end{matrix}\right.\)

với `A=1/2` ta có

\(\dfrac{1}{2}=\dfrac{-1}{\sqrt{a}+1}\\ < =>\sqrt{a}+1=-2\\ < =>\sqrt{a}=-3\left(vl\right)\)

với `A=-1/2` ta có

\(-\dfrac{1}{2}=\dfrac{-1}{\sqrt{a}+1}\\ < =>-\sqrt{a}-1=-2\\ < =>\sqrt{a}=1\\ < =>a=1\left(ktm\right)\)

`15*37*4+120*21+21*5*12`

`=60*37+60*2*21+60*21`

`=60(37+42+21)`

`=60*100`

`=6000`

`(2x-2)^3=8`

`(2x-2)^3=2^3`

`=>2x-2=2`

`x=2`

`3^7*5^7=(3*5)^7=15^7`

`S=1+2+2^2+2^3+...+2^2017`

`2S=2+2^2+2^3+2^4+...+2^2018`

`2S-S=(2+2^2+2^3+2^4+...+2^2018)-(1+2+2^2+2^3+...+2^2017)`

`S=2^2018 -1`

đổi `1` tá khăn `=12` khăn

1 khăn nặng số gam sợi là

`530:12=265/6`1(g)`

72 chiếc khăn như thế thì hết số ki lô gam sợi là

`265/6xx72=3180(g)=3,18(kg)`

`(5x-10)(3x-21)=0`

`=>5x-10=0` hoặc `3x-21=0`

`=>x=2` hoặc `x=7`

\(< =>\dfrac{30x^2}{60}+\dfrac{20y^2}{60}+\dfrac{15z^2}{60}=\dfrac{12x^2+12y^2+12z^2}{60}\\ < =>30x^2+20y^2+15z^2=12x^2+12y^2+12z^2\\ < =>18x^2+8y^2+3z^2=0\)

có \(\left\{{}\begin{matrix}x^2\ge0\\y^2\ge0\\z^2\ge0\end{matrix}\right.< =>\left\{{}\begin{matrix}18x^2\ge0\\8y^2\ge0\\3z^2\ge0\end{matrix}\right.\)

`=>18x^2+8y^2+3z^2>=0`

dấu ''='' xảy khi \(\left\{{}\begin{matrix}18x^2=0\\8y^2=0\\3z^2=0\end{matrix}\right.< =>\left\{{}\begin{matrix}x=0\\y=0\\z=0\end{matrix}\right.\)

\(9^4=\left(3^2\right)^4=3^8\) mà anh

`A=8^2*32^4=(2^3)^2*(2^5)^4=2^6*2^20=2^26`

`B=27^3*9^4*243=(3^3)^3*(3^2)^4*3^5=3^9*3^8*3^5=3^22`