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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

d: Ta có: \(E=\left(x-2\right)^3-\left(x+1\right)\left(x^2-x+1\right)+6\left(x-1\right)^2\)

\(=x^3-6x^2+12x-8-x^3-1+6x^2-12x+6\)

\(=-3\)

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

P=12(5^2+1)(5^4+1)(5^8+1)(5^16+1)

1/2P=24(5^2+1)(5^4+1)(5^8+1)(5^16+1)

1/2P=(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)

1/2P=(5^4-1)(5^4+1)(5^8+1)(5^16+1)

1/2P=(5^8-1)(5^8+1)(5^16+1)

1/2P=(5^16-1)(5^16+1)

1/2P=5^32-1

P=(5^32-1):1/2=2(5^32-1)

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

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

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

\(2P=\left(5^{16}-1\right)\left(5^{16}+1\right)\Rightarrow2P=5^{32}-1\Rightarrow P=\frac{5^{32}-1}{2}\)

mình nhầm phải là 2P mới đúng bn sửa lại rồi làm bt

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

(a+b+c)³=(a+b)³+3(a+b)²c+3(a+b)c²+c³

=a³+b³+3ab.(a+b)+3(a+b)²c+3(a+b)c²+c³

=a³+b³+c³+3(a+b)(ab+ac+bc+c²)

=a³+b³+c³+3(a+b)[a.(b+c)+c.(b+c)]

=a³+b³+c³+3(a+b)(b+c)(c+a) 

=>dpcm

P=12(5^2+1)(5^4+1)(5^8+1)(5^16+1)

=>2P=24(5^2+1)(5^4+1)(5^8+1)(5^16+1)

=(5²-1)(5²+1)(5⁴+1)(5⁸+1)(5¹⁶+1)

=(5⁴-1)(5⁴+1)(5⁸+1)(5¹⁶+1)

=(5⁸-1)(5⁸+1)(5¹⁶+1)

=(5¹⁶-1)(5¹⁶+1)

=5³²-1

==>P=(5³²-1)/2

thanks anh Triều!