\(a.\)\(10x+2^2.5=10\)

\(\Leftrightarrow10x+4.5=10\)

\(\Leftrightarrow10x+20=10\)

\(\Leftrightarrow10x=10-20\)

\(\Leftrightarrow10x=-10\)

\(\Leftrightarrow x=-10:10\)

\(\Leftrightarrow x=-1\)

\(b.\)\(125-5\left(4+x\right)=15\)

\(\Leftrightarrow5\left(4+x\right)=125-15\)

\(\Leftrightarrow5\left(4+x\right)=110\)

\(\Leftrightarrow4+x=110:5\)

\(\Leftrightarrow4+x=22\)

\(\Leftrightarrow x=22-4\)

\(\Leftrightarrow x=18\)

\(c.\)\(2^6+\left(218-x\right)=73\)

\(\Leftrightarrow64+\left(218-x\right)=73\)

\(\Leftrightarrow218-x=73-64\)

\(\Leftrightarrow218-x=9\)

\(\Leftrightarrow x=218-9\)

\(\Leftrightarrow x=209\)

a)10x+2².5=10

=>10x+4.5=10

=>10x+20 =10

=>10x       =10-20

=>10x       =-10

=>x           =-10:10

=>x           =-1

b)125-5(4+x)=15

=>5(4+x)       =125-15

=>5(4+x)       =110

=>x+4           =110:5

=>x+4           =22

=>x               =22-4

=>x               =18

c)2⁶+(218-x)=73

=>218-x       =73-64

=>218-x       =9

=>x              =218-9

=>x              =209

\(76-\left\{2\cdot\left[2\cdot5^2-\left(31-2\cdot3\right)\right]\right\}\)

\(=76-\left\{2\cdot\left[2\cdot25-\left(31-6\right)\right]\right\}\)

\(=75-\left[2\cdot\left(50-25\right)\right]\)

\(=76-\left(2\cdot25\right)\)

\(=76-50\)

\(=26\)

____________________

\(6^2\cdot10:\left\{780:\left[10^3-\left(2\cdot5^3+35\cdot14\right)\right]\right\}\)

\(=36\cdot10:\left\{780:\left[1000-\left(2\cdot125+490\right)\right]\right\}\)

\(=360:\left\{780:\left[1000-\left(250+490\right)\right]\right\}\)

\(=360:\left[780:\left(1000-740\right)\right]\)

\(=360:\left(780:260\right)\)

\(=360:3\)

\(=120\)

a: =76-{2*[2*25-31+6]}

=76-{2*[50-31+6]}

=76-2*25

=76-50=26

b: \(=360:\left\{\dfrac{780}{1000-2\cdot125-490}\right\}\)

\(=360:\dfrac{780}{260}\)

=360/3=120

\(G=x^4+10x^3+10x^2+10x+10\)
\(=x^4+10\left(x^3+x^2+x+1\right)\)
\(=\left(-9^4\right)+10\left[\left(-9\right)^3+\left(-9\right)^2+-9+1\right]\)
\(=6561+10\cdot-656\)
\(=6561-6560\)
\(=1\)

Thay `x=-9` vào biểu thức G:

`G=(-9)^4+10.(-9)^3+10.(-9)^2+10.(-9)+10`

`=6561-7290+810-90+10`

`=1`

Do \(x=-9\Rightarrow x+9=0\)

Ta có:

\(G=\left(x^4+9x^3\right)+\left(x^3+9x^2\right)+\left(x^2+9x\right)+\left(x+9\right)+1\)

\(=x^3\left(x+9\right)+x^2\left(x+9\right)+x\left(x+9\right)+\left(x+9\right)+1\)

\(=x^3.0+x^2.0+x.0+0+1=1\)

x=9

=>x+1=10

\(A=x^{10}-10x^9+10x^8-...+10x^2-10x+1\)

\(=x^{10}-x^9\left(x+1\right)+x^8\left(x+1\right)-...+x^2\left(x+1\right)-x\left(x+1\right)+1\)

\(=x^{10}-x^{10}-x^9+x^8+...+x^3+x^2-x^2-x+1\)

=-x+1

=-9+1=-8