Giúp mk vs , mk cần gấp
(a+b)(a-b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^16+b^16)
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Giúp mk vs , mk cần gấp
(a+b)(a-b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^16+b^16)
Cho \(a=b+1.\) Chứng minh: \(\left(a+b\right).\left(a^2+b^2\right).\left(a^4+b^4\right).\left(a^8+b^8\right)=a^{16}-b^{16}\)
\(a+b=1\)
\(\Rightarrow a-b=1\)
\(\Rightarrow VT=\left(a+b\right).\left(a^2+b^2\right).\left(a^4+b^4\right).\left(a^8+b^8\right)\)
\(=\left(a-b\right).\left(a+b\right).\left(a^2+b^2\right).\left(a^4+b^4\right).\left(a^8+b^8\right)\)
\(=\left(a^2-b^2\right).\left(a^2+b^2\right).\left(a^4+b^4\right).\left(a^8+b^8\right)\)
\(=\left(a^4-b^4\right).\left(a^4+b^4\right).\left(a^8+b^8\right)\)
\(=\left(a^8-b^8\right).\left(a^8+b^8\right)\)
\(=\left(a^{16}-b^{16}\right)=VP\)
\(\Rightarrow\) Đpcm.
P/s: Lần sau cậu viết đề rõ ràng ra nhé.
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rút gọn biểu thức
a) A=16^8 -1/(2+1)(2^2+1)(2^4+1)(2^8+1(3^16+1)
b) B=(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/9^16-1
giúp mk vs ah mk đang cần gấp ah
a) Ta có: \(A=\dfrac{16^8-1}{\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^{16}-1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{2^{32}-1}=1\)
b) Ta có: \(B=\dfrac{\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{9^{16}-1}\)
\(=\dfrac{\left(3^2-1\right)\cdot\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2\cdot\left(3^{32}-1\right)}\)
\(=\dfrac{\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2\cdot\left(3^{32}-1\right)}\)
\(=\dfrac{\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2\left(3^{32}-1\right)}\)
\(=\dfrac{\left(3^{16}-1\right)\left(3^{16}+1\right)}{2\left(3^{32}-1\right)}=\dfrac{1}{2}\)
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Bài 8 : Tìm x, biết :
a, x^2 - 10x + 16 = 0
b, x^2 - 11x - 26 = 0
c, 2x^2 + 7x - 4 = 0
Giúp mk vs ạ mk cần gấp
Bài 1: tính giá trị biểu thức
a) 6/7 + 5/8 : 5 - 3/16 .(-2) ^2
b) 2/3 + 1/3 . ( - 4/9 + 5/6) : 7/12
giúp mk vs mk đg cần gấp
6/7+5/8÷5-3/16×(-2)²
=6/7+1/8-3/4
=55/56-3/4
=13/56
b.2/3 + 1/3.( -4/9 + 5/6 ) : 7/12
=2/3 + 1/3. ( -8/18 + 15/18 ) : 7/12
=2/3 + 1/3 . 7/18 : 7/12
=2/3 + 7/54 : 7/12
= 2/3 + 2/9
=6/9 + 2/9
= 8/9
a)1 /2+ 1/4+1/8+1/16+1/32+...+1/256 giúp mk vs mk cần gấp nha😉
đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+...+\frac{1}{256}\)
=> A=\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+....+\frac{1}{2^8}\)
=> 2A=\(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+....+\frac{1}{2^7}\)
=> 2A-A=\(\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^7}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^8}\right)\)
=> A=\(1-\frac{1}{2^8}\)
MN GIUPS MK VS Ạ, MK XIN CẢM ƠN. MK ĐG CẦN RẤT GẤP Ạ.
B1) Cho các số thực dương a,b,c . CMR
a) a^2+b^2+c^2+abc+5>=3(a+b+c)
b) a^2+b^2+c^2 + 2abc +4>=2(a+b+c)+ab+bc+ca.
B2) Cho các số thực a; b; c: Chứng minh rằng
(a^2+1)(b^2+1)(c^2+1)>=5/16 .(a+b+c+d+1)^2.
MN GIÚP MK VS Ạ. MONG ADD DUYỆT Ạ . CẢM ƠN MN.
1. So sánh 2 số bằng cách vận dụng hằng đẳng thức:
a)A=1999.2001 Vs B=20002 b)A=216 vs B=(2+1)(22+1)(24+1)(28+1)
Các bn giải chi tiết nhé!! mk cần gấp!
a, \(A=1999.2001=\left(2000-1\right)\left(2000+1\right)=2000^2-1< 2000^2=B\)
Vậy A<B
b, \(B=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)=2^{16}-1< 2^{16}=A\)
Vậy A>B
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tính
a) 245 - 4 [ 16 : 8 + 2 ( 4 . 32 - 9 ) ]
b) 375 : 53 + ( 38 + 36 + 2 , 23 )
giúp mk nha mn mk cần gấp
Tính:
a,245-4×[16÷8+2×(4×3^2-9)]
=241×(4×27)
=241×108
=26028
b,375÷5^3+(3^8+3^6+2,2^3)
=375÷125+(7290+10,648)
=3+7300,648
=7303,648
a) 245 - 4 [ 16 : 8 + 2 ( 4 . 32 - 9 ) ] = 21
b) 375 : 53 + ( 38 + 36 + 2 , 23 ) = 7295.8
245-4[16:8+2(4.3^2-9)]
245-4[16:8+2(4.9-9)]
245-4[16:8+2(36-9)]
245-4[16:8+2.27]
245-4[2+2.27]
245-4[2+54]
245-4.56
245-224
21
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So sánh A và B biết A=1+1/2+1/3+1/4+...+1/15+1/16 với B=3 Giúp mk nhé, đang cần gấp lắm !
Anh qua câu hỏi của em đi, có ng trả lời mà, sao em hỏi nảy h anh ko trả lời
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\(A=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{15}+\frac{1}{16}\)
\(=1+\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)+\left(\frac{1}{6}+\frac{1}{7}+\frac{1}{8}\right)+\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}\right)+\left(\frac{1}{12}+\frac{1}{13}+\frac{1}{14}\right)\)
\(+\left(\frac{1}{15}+\frac{1}{16}\right)\)
Vì \(\frac{1}{6}+\frac{1}{7}+\frac{1}{8}< 3\times\frac{1}{6}=\frac{1}{2}\)
\(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}< 3\times\frac{1}{9}=\frac{1}{3}\)
\(\frac{1}{12}+\frac{1}{13}+\frac{1}{14}< 3\times\frac{1}{12}=\frac{1}{4}\)
\(\frac{1}{15}+\frac{1}{16}< 3\times\frac{1}{15}=\frac{1}{5}\)
\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}< 3\times\frac{1}{2}=\frac{3}{2}\)
\(\Rightarrow A=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{15}+\frac{1}{16}< 1+\frac{3}{2}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\)
\(\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+...+\frac{1}{15}+\frac{1}{16}< \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\)
P.s Mình tịt rồi , bạn cố gắng giải ra nhá ^.^!!
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