Ta có:

( 5 2 - 1).P = ( 5 2  – 1).12.( 5 2  + 1)( 5 4  + 1)( 5 8  + 1)( 5 16  + 1)

= 12.(  5 2  – 1).( 5 2  + 1)( 5 4 + 1)( 5 8  + 1)( 5 16 + 1)

= 12.(  5 4  - 1)(  5 4  + 1)(  5 8  + 1)( 5 16  + 1)

= 12.(  5 8  - 1)(  5 8  + 1)( 5 16  + 1)

= 12.(  5 16  - 1)( 5 16  + 1)

= 12.(  5 32  - 1)

Ta có: \(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(\Rightarrow P=\dfrac{24\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(\Rightarrow P=\dfrac{\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(\Rightarrow P=\dfrac{\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(\Rightarrow P=\dfrac{\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(\Rightarrow P=\dfrac{\left(5^{16}-1\right)\left(5^{16}+1\right)}{2}\)

\(\Rightarrow P=\dfrac{5^{32}-1}{2}\)

(5²-1)(5²+1) lại biến mất khi đem xuống z ạ

\(C=48\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)=2\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)=2\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)

\(=2\left(5^{128}-1\right)=2.5^{128}-2\)

c: Ta có: \(C=48\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\cdot\left(5^{32}+1\right)\left(5^{64}+1\right)\)

\(=2\cdot\left(5^2-1\right)\left(5^2+1\right)\cdot\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)

\(=2\cdot\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)

\(=2\cdot\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)

\(=2\cdot\left(5^{16}-1\right)\cdot\left(5^{16}+1\right)\cdot\left(5^{32}+1\right)\left(5^{64}+1\right)\)

\(=2\cdot\left(5^{32}-1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)

\(=2\cdot\left(5^{64}-1\right)\left(5^{64}+1\right)\)

\(=2\cdot\left(5^{128}-1\right)\)

\(=2\cdot5^{128}-2\)

Bài4:

=>x(x^2+1)=0

>x=0

Bài 5: 

=>\(3n^3+n^2+9n^2+3n-3n-1-4⋮3n+1\)

=>\(3n+1\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{0;-\dfrac{2}{3};\dfrac{1}{3};-1;1;-\dfrac{5}{3}\right\}\)

tử số =18.123+9.4567.2+3.5310.6=18.123+18.4567+18.5310

        =18(123+4567+5310)

        =18.10000=180000

mẫu số = 1+4+7+....+49+52+55+58-490

          =(1+58)+(4+55)+.....(28+31)-490

          =59+59+59+...+59-490(10 so 59)

         =100

suy ra A=180000:100=1800

Bài 4:

x^3+x=0

=>x(x^2+1)=0

=>x=0

Bài 5:

\(3n^3+10n^2-5⋮3n+1\)

\(\Leftrightarrow3n^3+n^2+9n^2-1-4⋮3n+1\)

=>\(3n+1\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{0;-\dfrac{2}{3};\dfrac{1}{3};-1;1;-\dfrac{5}{3}\right\}\)

Ta có: \(\dfrac{\sqrt{8-2\sqrt{12}}}{\sqrt{3}-1}\)

\(=\dfrac{\sqrt{\left(\sqrt{6}-\sqrt{2}\right)^2}}{\sqrt{3}-1}\)

\(=\sqrt{2}\)