\(A=\left(x^2-x+1\right)\left(x^4-x^2+1\right)\left(x^8-x^4+1\right)\left(x^{16}-x^8+1\right)\left(x^{32}-x^{16}+1\right)\)
Rút gọn A dưới dạng phân thức
Những câu hỏi liên quan
Rút gọn biểu thức:
\(\left(x+1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)\)
Rút gọn biểu thức với x - y = 1
\(\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\left(x^{16}+y^{16}\right)\)
Ta có \(x-y=1\)
\(=>x+y=\left(x+y\right).\left(x-y\right)\)
\(A=\left(x+y\right).\left(x-y\right).\left(x^2+y^2\right).\left(x^4+y^4\right)\)
\(A=\left(x^2-y^2\right).\left(x^2+y^2\right).\left(x^4+y^4\right)\)
\(A=\left(x^4-y^4\right).\left(x^4+y^4\right)\)
\(A=x^8-y^8\)
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= \(-\left[\left(x-y\right)\left(x^2-y^2\right)\left(x^4-y^4\right)\left(x^8-y^8\right)\left(x^{16}-y^{16}\right)\right]\)
= \(-\left[\left(x-y\right)\left(x-y\right)^2\left(x-y\right)^4\left(x-y\right)^8\left(x-y\right)^{16}\right]\)
= \(-\left(1\cdot1^2\cdot1^4\cdot1^8\cdot1^{16}\right)\)
= -1
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Rút gọn biểu thức:
a) \(\left(x+2\right)\left(x-2\right)-\left(x-3\right)\left(x+1\right)\)
b) \(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
a) \(\left(x+2\right)\left(x-2\right)-\left(x-3\right)\left(x+1\right)\)
\(=x^2-4-\left(x^2+x-3x-3\right)\)
\(=x^2-4-x^2-x+3x+3\)
\(=2x-1\)
b) \(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)=2^{32}-1\)
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Rút gọn biểu thức:
\(a.3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(b.x\left(2x^2-3\right)-x^2\left(5x+1\right)+x^2\)
\(c.3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)
a) 3(22+1)(24+1)(28+1)(216+1)
=(2+1)(2-1)(22+1)(24+1)(28+1)(216+1)
=(22-1)(22+1)(24+1)(28+1)(216+1)
=(24-1)(24+1)(28+1)(216+1)
.......
=(216-1)(216+1)=232-1
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Bài 1: Tính
\(A=3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)\)
Bài 2 : Chứng minh biểu thức sau viết được dưới dạng tổng của 2 bình phương
\(x^2+2\left(x+1\right)^2+3\left(x+2\right)^2+4\left(x+3\right)^2\)
1) CMR \(\frac{X^{32}+X^{16}+1}{X^2+X+1}\)= \(\left(X^2-X+1\right)\left(X^4-X^2+1\right)\left(X^8-X^4+1\right)\left(X^{16}-X^8+1\right)\)
2)\(Tinh\left(a-b\right)^{2017}Biet\left(a+b\right)=7;a.b=12\)(a<b)
Câu 1: Rút gọn các biểu thức sau:1. left(x+y-zright)^2+left(y-zright)^2+2zleft(z-yright)2. left(3x+4right)^2+left(x-4right)^2+2left(3x+4right)left(x-4right)3.left(3+1right)left(3^2+1right)left(3^4+1right)left(3^8+1right)left(3^{16}+1right)left(3^{32}+1right)4. 2xleft(2x-1right)^2-3xleft(x+3right)left(x-3right)-4xleft(x+1right)5. left(3+1right)left(3^2+1right)left(3^4+1right)left(3^8+1right)left(3^{16}+1right)left(3^{32}+1right)Câu 2: Tìm x1. 4left(x+1right)^2+left(2x-1right)^2-8left(x-1right)lef...
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Câu 1: Rút gọn các biểu thức sau:
1. \(\left(x+y-z\right)^2+\left(y-z\right)^2+2z\left(z-y\right)\)
2. \(\left(3x+4\right)^2+\left(x-4\right)^2+2\left(3x+4\right)\left(x-4\right)\)
3.\(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
4. \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)\)
5. \(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
Câu 2: Tìm x
1. \(4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x-1\right)\left(x+1\right)=1\)
2. \(\left(3x+1\right)^2+\left(5x-2\right)^2=34\left(x+2\right)\left(x-2\right)\)
3. \(\left(x+3\right)^2+\left(x-2\right)^2=2x^2\)
4. \(4x^2-9-x\left(2x-3\right)=0\)
5. \(4x^2-12x+9=0\)
Câu 3: Tìm GTNN
D = \(\left(2x-1\right)^2+\left(x+2\right)^2\)
Câu 4: Cho \(a^2+b^2+c^2=ab+bc+ac\) . Chứng minh rằng a=b=c
Rút gọn biểu thức:
a) \(\left(x+2\right)\left(x-2\right)-\left(x-3\right)\left(x+1\right)\)
b) \(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(\left(x+2\right)\left(x-2\right)-\left(x-3\right)\left(x+1\right)\)
\(=x^2-4-\left(x^2-2x-3\right)\)
\(=2x-1\)
\(\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)
\(=2^{32}-1\)
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1) Phân tích:
a)\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1\)
b)\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
a)(x+1)(x+2)(x+3)(x+4)+1
=(x+1)(x+4)(x+2)(x+3)+1
=(x2+5x+4)(x2+5x+6)+1
Đặt a=(x2+5x+4) thì (x2+5x+4)(x2+5x+6)+1
= a.(a+2)+1
=a2+2a+1
=(a+1)2
Thay: =(x2+5x+4+1)2
=(x2+5x+5)2
b)(x+2)(x+4)(x+6)(x+8)+16
=(x+2)(x+8)(x+4)(x+6)+16
=(x2+10x+16)(x2+10x+24)+16
Đặt a=(x2+10x+16) thì (x2+10x+16)(x+5x+24)+1
= a.(a+8)+16
=a2+8x+16
=(a+4)2
Thay: =(x2+10x+16+4)2
=(x2+5x+20)2
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App giải toán không cần nhập đề chỉ cần chụp ảnh cho cả nhà đây: https://www.facebook.com/watch/?v=485078328966618
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a)(x+1)(x+2)(x+3)(x+4)+1
=[(x+1)(x+4][(x+2)(x+3)]+1
=(x2+5x+4)(x2+5x+6)+1
Đặt a=(x2+5x+4)
Ta có: (x2+5x+4)(x2+5x+6)+1
= a.(a+2)+1
=a2+2a+1
=(a+1)2
=(x2+5x+4+1)2
=(x2+5x+5)2
b)(x+2)(x+4)(x+6)(x+8)+16
=(x+2)(x+8)(x+4)(x+6)+16
=(x2+10x+16)(x2+10x+24)+16
Đặt a=(x2+10x+16)
Ta có:(x2+10x+16)(x+5x+24)+1
= a.(a+8)+16
=a2+8x+16
=(a+4)2
=(x2+10x+16+4)2
=(x2+5x+20)2
Mk yêu bé Shin-Conan lém
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