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VT
1
MA
20 tháng 9 2016
\(D=8\left(7^8+1\right)\left(7^4+1\right)\left(7^2-1\right)\)
\(D=\frac{4}{25}\left(7^2+1\right)\left(7^2-1\right)\left(7^4+1\right)\left(7^8+1\right)\)
\(D=\frac{4}{25}\left(7^4-1\right)\left(7^4+1\right)\left(7^8+1\right)\)
\(D=\frac{4}{25}\left(7^8-1\right)\left(7^8+1\right)\)
\(D=\frac{4}{25}\left(7^{16}-1\right)\)
Vì: \(\frac{4}{25}\left(7^{16}-1\right)< 7^{16}-1\Rightarrow D< C\)
KL
1
HH
26 tháng 6 2018
Giải:
a) \(M=\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(\Leftrightarrow3M=3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(\Leftrightarrow3M=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(\Leftrightarrow3M=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(\Leftrightarrow3M=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(\Leftrightarrow3M=\left(2^{16}-1\right)\left(2^{16}+1\right)\)
\(\Leftrightarrow3M=2^{32}-1\)
\(\Leftrightarrow M=\dfrac{2^{32}-1}{3}\)
Vậy ...
b) \(N=16\left(7^2+1\right)\left(7^4+1\right)\left(7^8+1\right)\left(7^{16}+1\right)\)
\(\Leftrightarrow3N=48\left(7^2+1\right)\left(7^4+1\right)\left(7^8+1\right)\left(7^{16}+1\right)\)
\(\Leftrightarrow3N=\left(7^2-1\right)\left(7^2+1\right)\left(7^4+1\right)\left(7^8+1\right)\left(7^{16}+1\right)\)
\(\Leftrightarrow3N=\left(7^4-1\right)\left(7^4+1\right)\left(7^8+1\right)\left(7^{16}+1\right)\)
\(\Leftrightarrow3N=\left(7^8-1\right)\left(7^8+1\right)\left(7^{16}+1\right)\)
\(\Leftrightarrow3N=\left(7^{16}-1\right)\left(7^{16}+1\right)\)
\(\Leftrightarrow3N=7^{32}-1\)
\(\Leftrightarrow N=\dfrac{7^{32}-1}{3}\)
Vậy ...
KN
12 tháng 9 2019
Làm dễ hiểu chút
\(A=\left(2^2+4^2+...+100^2\right)-\left(1^2+3^2+...+99^2\right)\)
\(=\left(2^2-1^2\right)+\left(4^2-3^2\right)+...+\left(100^2-99^2\right)\)
\(=\left(2+1\right)\left(2-1\right)+\left(4+3\right)\left(4-3\right)+...+\left(100-99\right)\left(99+100\right)\)
\(=3+7+...+199\)
\(B=3^8.7^8-\left(21^4-1\right)\left(21^4+1\right)\)
\(=21^8-\left(21^8-1\right)=1\)
Vậy A > B
TT
5
12 tháng 8 2016
\(A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)=2^{32}-1\)
\(B=2^{32}\)
=> \(A< B\)
12 tháng 8 2016
ta có A= \(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
=(2-1)(2+1)\(\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
=\(2^{32}-1\) (ấp dụng các hằng đẳng thức )
=> A=232-1
B=232
=> A<B
SM
1 tháng 9 2018
a) A = 20152
B = 2014.2016 = ( 2015 - 1 ) . ( 2015 + 1 ) = 20152 - 1
Vì 20152 > 20152 - 1
=> A > B
b) C = 316 - 1
D = 8. ( 32 + 1 ).( 34 + 1 ). ( 38 + 1 )
= ( 32 - 1 ).( 32 + 1 ).( 34 + 1 ). ( 38 + 1 )
= ( 34 - 1 ).( 34 + 1 ). ( 38 + 1 )
= ( 38 - 1 ) . ( 38 + 1 )
= 316 - 1
Vì 316 - 1 = 316 - 1
=> C = D
13 tháng 7 2017
\(\left(x+4\right)\left(x^2-4x+16\right)-x\left(x-4\right)^2=8\left(x-3\right)\left(x+3\right)\)3)
\(\Leftrightarrow x^3+4^3-x\left(x-4\right)^2=8\left(x^2-3^2\right)\)
\(\Leftrightarrow x^3+64-x\left(x^2-8x+16\right)=8x^2-72\)
\(\Leftrightarrow x^3+64-x^3+8x^2-16x-8x^2-72=0\)
\(\Leftrightarrow-16x-8=0\)
\(\Leftrightarrow-8\left(2x-1\right)=0 \)
\(\Rightarrow2x-1=0\)
\(\Leftrightarrow2x=1\)
\(\Leftrightarrow x=\frac{1}{2}\)
Vậy \(x=\frac{1}{2}\)
27 tháng 8 2019
=a, (x-3)(x+3)-(x-7)(x+7)= x2 - 9 - x2 + 7
= -2
b, (4x-5)2+(3x-2)2-2(4x+5)(3x-2)= (4x-5)2 - 2(4x+5)(3x-2) + (3x-2)2
= ( 4x - 5 - 3x + 2 )2
= ( x - 3 )2
c, 2(3x-y)(3x+y)+(3x-y)2+(3x+y)2= 2(3x-y)(3x+y)+(3x-y)2+(3x+y)2
= (3x-y)2+ 2(3x-y)(3x+y)+ (3x+y)2
= ( 3x - y + 3x + y )2
= ( 6x )2
= 36x2
d, (x-y+z)2+(z-y)2+2(x-y+z+2(x-y+z)(y-z-y+z)(y-z)
27 tháng 8 2019
1, rút gọn
a, (x-3)(x+3)-(x-7)(x+7)
= x^2 - 9 - (x^2 - 49)
= x^2 - 9 - x^2 + 49
= 40
b, (4x-5)2+(3x-2)2-2(4x+5)(3x-2)
= 16x^2 - 40x + 25 + 9x^2 - 12x + 4 - 2(12x^2 - 8x + 15x - 10)
= 25x^2 - 52x + 29 - 24x^2 + 16x - 30x + 20
= x^2 - 66x + 49
c, 2(3x-y)(3x+y)+(3x-y)2+(3x+y)2
= 2(9x^2 - y^2) + 9x^2 - 6xy + y^2 + 9x^2 + 6xy + y^2
= 18x^2 - 2y^2 + 18x^2 + 2y^2
= 36x^2
d, (x-y+z)2+(z-y)2+2(x-y+z+2(x-y+z)(y-z-y+z)(y-z)
= dài vl
bn có nick bingbe ko