a.\(\left(a+5\right)^2+2\left(a+5\right)\left(\dfrac{1}{2}-a\right)+\left(\dfrac{1}{2}-a\right)^2\)

\(=\left(a+5+\dfrac{1}{2}-a\right)^2\)

\(=\left(\dfrac{11}{2}\right)^2\)

\(=\dfrac{121}{4}\)

`1.`

`a.`\(\left(a+5\right)^2+2\left(a+5\right)\left(\dfrac{1}{2}-a\right)+\left(1-a\right)^2\)

\(=\left(a+5+1-a\right)^2\)

\(=6^2=36\)

`b.`\(\dfrac{x^2-16+2xy+y^2}{3x^2-12x+3xy}\)

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

\(=\dfrac{\left(x+y-4\right)\left(x+y+4\right)}{3x\left(x+y-4\right)}\)

\(=\dfrac{x+y+4}{3x}\)

`2.` 

`a.`\(5x-15x^2=0\)

`<=>5x(1-3x)=0`

\(\Leftrightarrow\left[{}\begin{matrix}5x=0\\1-3x=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{3}\end{matrix}\right.\)

`b.x^2+9=6x`

`<=>x^2-6x+9=0`

`<=>(x-3)^2=0`

`<=>x-3=0`

`<=>x=3`

`3.`\(\dfrac{2x^3-7x^2+7x-2}{x-2}=2x^2-3x+1\)

`4.` 

`a.x^4+1`

`=(x^2)^2+1`

`b.4x^4+81`

`=(2x^2)^2+9^2`

\(V=3\left(l\right)\) \(\Rightarrow m=3.1=3\left(kg\right)\) 

Nhiệt lượng cần để đun sôi nước:

\(Q_i=A_i=m.c.\Delta t=3.4200.\left(100-25\right)=945000\left(J\right)\)

Ta có:

\(H=\dfrac{A_i}{A_{tp}}.100=90\left(\%\right)\)

\(\Rightarrow A_{tp}=\dfrac{945000.100}{90}=1050000\left(J\right)\)

Thời gian đun sôi nước:

\(A_{tp}=P.t\Rightarrow t=\dfrac{A_{tp}}{P}=\dfrac{1050000}{1000}=1050\left(s\right)\)