rut gon P= (1-1/1+2).(1-1/1+2+3).(1-1/1+2+3+4)...(1/1+2+3+4+..+100)
Rut gon \(A=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)....\left(\frac{1}{100^2}-1\right)\)
rut gon A= 1*4/2*3+2*5/2*4+3*6/4*5+...+98*101/99*100
rut gon bieu thuc
1/(1^4+1^2+1)+2/(2^4+2^2+1)+3/(3^4+3^2+1)+...+2014/(2014^4+2014^2+2014)=...
{giup minh vs}
rut gon bieu thuc
3(2^2+1).(2^4+1)...(2^64+1)+1
\(3\left(2^2+1\right).\left(2^4+1\right)...\left(2^{64}+1\right)+1\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)
\(=\left(2^4-1\right)\left(2^4+1\right)....\left(2^{64}+1\right)+1\)
\(=\left(2^8-1\right).\left(2^8+1\right)\left(2^{16}+1\right)....\left(2^{64}+1\right)+1\)
\(=\left(2^{64}-1\right).\left(2^{64}+1\right)+1\)
\(=2^{64}-1+1=2^{64}\)
Vậy : \(3\left(2^2+1\right).\left(2^4+1\right)...\left(2^{64}+1\right)+1=2^{64}\)
Rut gon bieu thuc
\(\frac{1}{1^4+1^2+1}+\frac{2}{2^4+2^2+1}+\frac{3}{3^4+3^2+1}+...+\frac{2014}{2014^4+2014^2+1}\)
Áp dụng a/(a^4+a^2+1)=1/2.(1/(a^2-a+1)-1/(a^2+a+1)) ta được
A=1/2.(1/(1^2-1+1)-1/(1^2+1+1)+1/(2^2-2+1)-1/(2^2+2+10)+...+1/(2014^2-2014+1)-1/(2014^2+2014+1))
A=1/2.(1-1/(2014^2+2014+1))
A=-2029105/4058211
(CHẮC CHẮN ĐÚNG)
Rut gon bieu thuc
3(2^2+1)(2^4+1)(2^8+1)(2^16+1)
=\(\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
=\(\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
=...=2^32-1
nhân hết ra là xong:))
bài về nhà hs phải tự làm
Cái bước (22-1)(22 + 1)(24 +1)(216+1) làm như thế nào mà ra vậy
rut gon bieu thuc:(1/2+1)(1/3+1)(1/4+1).....(1/99+1)
Bài này có rắc rối đâu em?
Thực hiện phép tính trong ngoặc lại là ra dạng (n+1)/n.
1 dãy các số liên tục kéo dài nhân với nhau thì triệt tiêu là xong!
Chúc em học tốt!
Rut gon bieu thuc sau
3(2*2+1)(2*4+1)(2*8+1)(2*16+1)
1) CMR: 543-54 khong la so chinh phuong
2) Tim x:
2(x-2).(x+3)-x2+4=0
3) Rut gon
a)2(x+1)2-3(x-1)2+(x+2).(5-x)
b)(3x-1)3+(3x-1)3-6x2+9
4) A= (x-5).(x+2)+3.(x-2).(x+2)-(3x-1)2+5x2
a) rut gon A
b) tinh a khi x =1/2
\(2\left(x-2\right)\left(x+3\right)-x^2+4=0\)
\(2\left(x^2+3x-2x-6\right)-x^2+4=0\)
\(2x^2+6x-4x-12-x^2+4=0\)
\(x^2+2x-8=0\)
\(x^2+4x-2x-8=0\)
\(x\left(x+4\right)-2\left(x+4\right)=0\)
\(\left(x+4\right)\left(x-2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+4=0\rightarrow x=\left(-4\right)\\x-2=0\rightarrow x=2\end{cases}}\)
3/
a/ \(2\left(x+1\right)^2-3\left(x-1\right)^2+\left(x+2\right)\left(5-x\right)\)
\(=2\left(x^2+2x+1\right)-3\left(x^2-2x+1\right)+\left(5x-x^2+10-2x\right)\)
\(=2x^2+4x+2-3x^2+6x-3+5x-x^2+10-2x\)
\(=-2x^2+13x+9\)
b/ \(\left(3x-1\right)^3+\left(3x-1\right)^3-6x^2+9\)
\(=2\left(3x-1\right)^3-6x^2+9\)
\(=2\left(\left(3x\right)^3-3\left(3x\right)^2\cdot1+3\cdot3x\cdot1-1\right)-6x^2+9\)
\(=2\left(27x^3-27x^2+9x-1\right)-6x^2+9\)
\(=54x^3-54x^2+18x-2-6x^2+9\)
\(=54x^3-60x^2+18x+7\)
Số hơi dài, nên dễ tính sai -,- tính mik hay cẩu thả có j sai ibbb ạ
2) 2.(x - 2).(x + 3) - x2 + 4 = 0
<=> x2 + 2x - 8 = 0
<=> (x - 2).(x + 4) = 0
x - 2 = 0 hoặc x + 4 = 0
x = 0 + 2 x = 0 - 4
x = 2 x = -4
=> x = 2 hoặc x = -4
3) a) 2.(x + 1)2 - 3.(x - 1)2 + (x + 2).(5 - x)
= 2.(x2 + 2x + 1) - 3.(x2 - 2x + 1) + (x + 2).(5 - x)
= 2x2 + 4x + 2 - 3x2 + 6x - 3 + (x + 2).(5 - x)
= 2x2 + 4x + 2 - 3x2 + 6x - 3 + 3x - x2 + 10
= (2x2 - 3x2 - x2) + (4x + 6x + 3x) + (2 - 3 + 10)
= -2x2 + 13x + 9
b) (3x - 1)3 + (3x - 1)3 - 6x2 + 9
= 2.(3x - 1)3 - 6x2 + 9
= 2.(27x3 - 27x2 + 9x - 1) - 6x2 + 9
= 54x3 - 54x2 + 18x - 2 - 6x2 + 9
= 54x3 + (-54x2 - 6x2) + 18x + (-2 + 9)
= 54x3 - 60x + 18x + 7
4) a) A = (x - 5).(x + 2) + 3.(x - 2).(x + 2) - (3x - 1)2 + 5x2
A = (x - 5).(x + 2) + 3.(x - 2).(x + 3) - (9x2 - 6x + 1) + 5x2
A = x2 - 3x - 10 + 3x2 - 12 - (9x2 - 6x + 1) + 5x2
A = x2 - 3x - 10 + 3x2 - 12 - 9x2 + 6x - 1 + 5x2
A = (x2 + 3x2 - 9x2 + 5x2) + (-3x + 6x) + (-10 - 12 - 1)
A = 3x - 23 (1)
b) Thay x = 1/2 vào (1), ta có:
A = 3x - 23 = 3.(1/2) - 23
= 3/2 - 23
= -43/2
A khi x = 1/2 là -43/2