goi y nha A=1/2.(3^2-1)(3^2+1)....(3^32+1)

Đặt \(A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\).Ta có : 

\(=>\left(3-1\right)A=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=>2A=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=>2A=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

...............................................................................

Cuối cùng \(=>2A=3^{64}-1\).

\(=>A=\frac{3^{64}-1}{2}\)

Đặt \(A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(\Rightarrow2A=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=...........................................\)

\(=\left(3^{32}-1\right)\left(3^{32}+1\right)=3^{64}-1\)

\(\Rightarrow A=\frac{3^{64}-1}{2}\)

\(8.\left(3^2+1\right).\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-3^{32}\)

\(=\left(3^2-1\right).\left(3^2+1\right).\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-3^{32}\)

\(=\left(3^4-1\right).\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-3^{32}\)

\(=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)-3^{32}\)

\(=\left(3^{16}-1\right)\left(3^{16}+1\right)-3^{32}=3^{32}-1-3^{32}=-1\)

Đặt \(A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=4\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

Ta có: \(2.A=8\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)=\left(3^{16}-1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)=\left(3^{32}-1\right)\left(3^{32}+1\right)\)

\(=3^{64}-1=>A=\frac{3^{64}-1}{2}\)
 

Ta có: 3 + 1 = (3^2 - 1)/(3 - 1) 
3^2 + 1 = (3^4 - 1)/(3^2 - 1) 
3^4 + 1 = (3^8 - 1)/(3^4 - 1) 
3^8 + 1 = (3^16 - 1)/(3^8 - 1) 
3^16 + 1 = (3^32 - 1)/(3^16 - 1) 
3^32 + 1 = (3^64 - 1)/(3^32 - 1) 

(3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1) 
=(3^2 - 1)/(3 - 1).(3^4 - 1)/(3^2 - 1).(3^8 - 1)/(3^4 - 1).(3^32 - 1)/(3^16 - 1).(3^64 - 1)/(3^32 - 1) 
=(3^64 - 1)/(3 - 1) 
=(3^64 - 1)/2

Đặt biểu thức đó là A

(3-1) A= (3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1) (3^32+1)

2 A= (3^2-1)(3^2+1)(3^4+1)..............................................

2A = (3^4-1)(3^4+1)(3^8+1)                   ............................

2A= (3^8-1)(3^8+1)(3^16+1)                                  .............

2A = (3^16-10(3^16+1)(3^32+1)

2A = (3^32-1)(3^32+1)

2A= 3^64-1

A= (3^64-1) / 2

#)Giải :

\(=\frac{\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)}{8}\)

\(=\frac{\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)}{8}\)

\(=\frac{\left(3^{16}-1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)}{8}\)

\(=\frac{\left(3^{32}-1\right)\left(3^{32}+1\right)}{8}\)

\(=\frac{3^{64}-1}{8}\)

Đặt A

Rút gọn: (3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)
A=(3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)
2A=2(3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)
2A=(3-1)(3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)
2A=(3^2-1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)
2A=(3^4-1)(3^4 + 1)(3^8 + 1)(3^16 + 1)(3^32 + 1)
2A=(3^8-1)(3^8 + 1)(3^16 + 1)(3^32 + 1)
2A=(3^16-1)(3^16 + 1)(3^32 + 1)
2A=(3^32 - 1)(3^32 + 1)
2A=3^64-1
=>A=(3^64-1) /2

Lời giải :

\(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\frac{1}{2}\cdot\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\frac{1}{2}\cdot\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\frac{1}{2}\cdot\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\frac{1}{2}\cdot\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\frac{1}{2}\cdot\left(3^{16}-1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\frac{1}{2}\cdot\left(3^{32}-1\right)\left(3^{32}+1\right)\)

\(=\frac{1}{2}\cdot\left(3^{64}-1\right)\)

\(=\frac{3^{64}-1}{2}\)

1 tính giá trị biểu thức 

a) Cho x-y=7.Tính giá trị của biểu thức A=x(x+2)+y(y+2)-2xy+37

b) cho x+y=10 và x²+y²=10.Tính x³+y³

giúp mình bài này nữa

[Toán 8] Rút gọn $ (3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)$ | HOCMAI Forum - Cộng đồng học sinh Việt Nam

Đặt biểu thức đã cho là A.

Ta có: 2A = (3 - 1) * (3 + 1) * (3^2 + 1) * .... * (3^64 + 1)

= (3^2 - 1) * (3^2 + 1) * ... * (3^64 + 1) (hằng đẳng thức a^2 - b^ 2 = (a+b)(a-b))

Rút gọn triệt tiêu ta được 2A=3^64 - 1

=> A = (3^64 - 1)/2

mk chịu