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d, D = 402 - 282 + 322 +80.32
D = (402 + 2.40.32 + 322) - 282
D = (40 + 32)2 - 282
D = (40 + 32 - 28)(40 + 32 + 28)
D = 44.100
D = 4400
e, E = 10.80,5 + 10.19,5 - 8.20,5 - 8. 79,5
E = 10.(80,5 + 19,5) - 8.( 20,5 + 79,5)
E = 10.100 - 8.100
E = 100.(10-8)
E = 200
F = 502 - 182 + 322 + 100.32
F = (502 - 182) + 32.( 32 + 100)
F = (50 -18)(50+18) + 32. 132
F = 32.68 + 32.132
F = 32.( 68 + 132)
F = 32. 200
F = 6400
a) \(x^2-5x+6\)
\(=x^2-2x-3x+6=x\left(x-2\right)-3\left(x-2\right)=\left(x-2\right)\left(x-3\right)\)
b) \(x^2-9x+18=x^2-3x-6x+18\)
\(=x\left(x-3\right)-6\left(x-3\right)=\left(x-3\right)\left(x-6\right)\)
c) \(x^2-6x+5=x^2-x-5x+5\)
\(=x\left(x-1\right)-5\left(x-1\right)=\left(x-1\right)\left(x-5\right)\)
d) \(3x^2+5x-30=3\left(x^2+\dfrac{5x}{3}-10\right)=3\left(x^2+2.x.\dfrac{5}{6}+\dfrac{25}{36}-\dfrac{5347}{500}\right)\)
Câu này bạn xem lại đề nha
e) \(3x^2-5x-2=3x^2-6x+x-2\)
\(3x\left(x-2\right)+x-2=\left(x-2\right)\left(3x+1\right)\)
a) 2( x - 1 )2 - 4( 3 + x )2 + 2x( x - 5 )
= 2( x2 - 2x + 1 ) - 4( 9 + 6x + x2 ) + 2x2 - 10x
= 2x2 - 4x + 2 - 36 - 24x - 4x2 + 2x2 - 10x
= ( 2x2 - 4x2 + 2x2 ) + ( -4x - 24x - 10x ) + ( 2 - 36 )
= -38x - 34
b) 2( 2x + 5 )2 - 3( 4x + 1 )( 1 - 4x )
= 2( 4x2 + 20x + 25 ) + 3( 4x + 1 )( 4x - 1 )
= 8x2 + 40x + 50 + 3( 16x2 - 1 )
= 8x2 + 40x + 50 + 48x2 - 3
= 56x2 + 40x + 47
c) ( x - 1 )3 - x( x - 3 )2 + 1
= x3 - 3x2 + 3x - 1 - x( x2 - 6x + 9 ) + 1
= x3 - 3x2 + 3x - x3 + 6x2 - 9x
= 3x2 - 6x
d) ( x + 2 )3 - x2( x + 6 )
= x3 + 6x2 + 12x + 8 - x3 - 6x2
= 12x + 8
e) ( x - 2 )( x + 2 ) - ( x + 1 )3 - 2x( x - 1 )2
= x2 - 4 - ( x3 + 3x2 + 3x + 1 ) - 2x( x2 - 2x + 1 )
= x2 - 4 - x3 - 3x2 - 3x - 1 - 2x3 + 4x2 - 2x
= -3x3 + 2x2 - 5x - 5
f) ( a + b - c )2 - ( b - c )2 - 2a( b - c )
= [ ( a + b ) - c ]2 - ( b2 - 2bc + c2 ) - 2ab + 2ac
= [ ( a + b )2 - 2( a + b )c + c2 ] - b2 + 2bc - c2 - 2ab + 2ac
= a2 + 2ab + b2 - 2ac - 2bc + c2 - b2 + 2bc - c2 - 2ab + 2ac
= a2
a) \(2\left(x-1\right)^2-4\left(3+x\right)^2+2x\left(x-5\right)\)
Dùng hẳng đẳng thức thứ nhất + hai :
= \(2\left(x^2-2\cdot x\cdot1+1^2\right)-4\left(3^2+2\cdot3\cdot x+x^2\right)+2x^2-10x\)
= \(2\left(x^2-2x+1\right)-4\left(9+6x+x^2\right)+2x^2-10x\)
= \(2x^2-4x+2-36-24x-4x^2+2x^2-10x\)
= \(-38x-34\)
b) 2(2x + 5)2 - 3(4x + 1)(1 - 4x)
Dùng đẳng thức thứ 1 + 3
= 2[(2x)2 + 2.2x.5 + 52 ] - (-3)[(4x)2 - 12 ]
= 2(4x2 + 20x + 25) - (-3).(16x2 - 1)
= 8x2 + 40x + 50 - (3 - 48x2)
= 8x2 + 40x + 50 - 3 + 48x2
= 56x2 + 40x + 47
c) (x - 1)3 - x(x - 3)2 + 1
Dùng đẳng thức 2 + 5:
= x3 - 3.x2.1 + 3.x.12 - 13 - x(x2 - 2.x.3 + 32) + 1
= x3 - 3x2 + 3x - 1 - x3 + 6x2 - 9x + 1
= (x3 - x3) + (-3x2 + 6x2) + (3x - 9x) + (-1 + 1)
= 3x2 - 6x
d) (x + 2)3 - x2(x + 6)
= x3 + 3.x2.2 + 3.x.22 + 23 - x3 - 6x2
= x3 + 6x2 + 12x + 8 - x3 - 6x2
= (x3 - x3) + (6x2 - 6x2) + 12x + 8 = 12x + 8
e) Dùng đẳng thức thứ 3,4 và 2
= x2 - 4 - (x3 + 3.x2.1 + 3.x.12 + 13) - 2x(x2 - 2.x.1 + 12)
= x2 - 4 - (x3 + 3x2 + 3x + 1) - 2x3 + 4x2 - 2x
= x2 - 4 - x3 - 3x2 - 3x - 1 - 2x3 + 4x2 - 2x
= (x2 - 3x2 + 4x2) + (-4 - 1) + (-x3 - 2x3) + (-3x - 2x)
= 2x2 - 5 - 3x3 - 5x
f) Đặt \(a+b-c=A\)
\(b-c=B\)
= \(A^2-B^2-2AB\)
= \(A^2-2AB+\left(-B\right)^2\)
\(=A^2-2AB+B^2\)
= (A - B)2
= (a + b - c - (b - c))2
= (a + b - c - b + c)2
= a2
Bài 2:
a: \(\Leftrightarrow\left(x-5\right)\left(x+5\right)-\left(x+5\right)=0\)
=>(x+5)(x-6)=0
=>x=-5 hoặc x=6
b: \(\Leftrightarrow4x^2-4x+1-4x^2+1=0\)
=>-4x+2=0
hay x=1/2
c: \(\Leftrightarrow\left(x^2+4\right)\left(x^2-1\right)=0\)
=>x=1 hoặc x=-1
1 + 2xy - x2 - y2
= 1 - ( x2 - 2xy + y2 )
= 12 - ( x - y )2
= [ 1 - ( x - y ) ][ 1 + ( x - y ) ]
= ( y - x + 1 )( x - y + 1 )
a2 + b2 - c2 - d2 - 2ab + 2cd
= ( a2 - 2ab + b2 ) - ( c2 - 2cd + d2 )
= ( a - b )2 - ( c - d )2
= [ ( a - b ) - ( c - d ) ][ ( a - b ) + ( c - d ) ]
= ( a - b - c + d )( a - b + c - d )
a3b3 - 1
= ( ab )3 - 13
= ( ab - 1 )[ ( ab )2 + ab.1 + 12 ]
= ( ab - 1 )( a2b2 + ab + 1 )
x2( y - z ) + y2( z - x ) + z2( x - y )
= z2( x - y ) + x2y - x2z + y2z + y2x
= z2( x - y ) + ( x2y - y2x ) - ( x2z - y2z )
= z2( x - y ) + xy( x - y ) - z( x2 - y2 )
= z2( x - y ) + xy( x - y ) - z( x + y )( x - y )
= ( x - y )[ z2 + xy - z( x + y ) ]
= ( x - y )( z2 + xy - zx - zy )
= ( x - y )[ ( z2 - zx ) - ( zy - xy ) ]
= ( x - y )[ z( z - x ) - y( z - x ) ]
= ( x - y )( z - x )( z - y )
Ta có: a + b + c = 0
=> (a + b + c)2 = 0
=> a2 + b2 + c2 + 2(ab + bc + ac) = 0
=> 14 + 2(ab + bc + ac) = 0
=> 2ab + 2bc + 2ac = -14
=> (2ab + 2bc + 2ac)2 = 196
=> 4a2b2 + 4a2c2 + 4b2c2 + 8ab2c + 8a2bc + 8abc2 = 196
=> 4(a2b2 + b2c2 + c2a2) + 8abc(b + a + c) = 196
=> 4(a2b2 + b2c2 + c2a2) = 196
=> 2(a2b2 + b2c2 + c2a2) = 98
Có: a2 + b2 + c2 = 14
=> (a2 + b2 + c2)2 = 196
=> a4 + b4 + c4 + 2(a2b2 + b2c2 + a2c2) = 196
Mà 2(a2b2 + b2c2 + a2c2) = 98
=> a4 + b4 + c4 = 98
Vậy a4 + b4 + c4 = 98
1. 3A = 3^2 + 3^3 + 3^4 + ... + 3^100 + 3^ 101
=> 3A - A = (3^2 + 3^3 + 3^4 + ... + 3^100 + 3^ 101) - (3 + 3^2 + 3^3 + 3^4 + ... + 3^100 )
=> 2A = 3^101 - 3 => 2A + 3 = 3^101 vậy n = 101
2. 2A = 8 + 2 ^ 3 + 2^4 + ... + 2^20 + 2^21
=> 2A - A = (8 + 2 ^ 3 + 2^4 + ... + 2^20 + 2^21) - (4+ 2^2 + 2 ^ 3 + 2^4 + ... + 2^20 )
=> A = 2^21 là một lũy thừa của 2
3.
a) 3A = 3 + 3^2 + 3^3 + 3^4 + ... + 3^100 + 3^ 101
=> 3A - A = (3 + 3^2 + 3^3 + 3^4 + ... + 3^100 + 3^ 101) - (1 + 3 + 3 ^2 + 3 ^ 3 + ... + 3 ^100)
=> 2A = 3^101 - 1 => A = (3^101 - 1)/2
b) 4B = 4 + 4 ^ 2 + 4 ^3 + 4 ^ 4 + ... + 4 ^ 100 + 4^ 101
=> 4B - B = (4 + 4 ^ 2 + 4 ^3 + 4 ^ 4 + ... + 4 ^ 100 + 4^ 101) - (1 + 4 + 4 ^ 2 + 4 ^3 + 4 ^ 4 + ... + 4 ^ 100 )
=> 3B = 4^101 - 1 => B = ( 4^101 - 1)/2
c) Bạn hãy xem lại đề ý c xem quy luật như thế nào nhé.
d) 3D = 3^101 + 3^ 102 + 3^ 103 + ... + 36 150 + 3^ 151
=> 3D - D = (3^101 + 3^ 102 + 3^ 103 + ... + 36 150 + 3^ 151) - (3 ^100 + 3 ^ 101 + 3 ^ 102 + .... + 3 ^ 150)
=> 2D = 3^ 151 - 3^100 => D = ( 3^ 151 - 3^100)/2
mu là mũ nha giúp tui vứi
a) \(82^2-18^2=\left(82-18\right)\left(82+18\right)=64.100=6400\)
b) \(26^2+52.24+24^2=26^2+2.26.24+24^2=\left(26+24\right)^2=50^2=2500\)
c) \(\dfrac{93^3+78^3}{171}-93.78=\dfrac{\left(93+78\right)\left(93^2-93.78+73^2\right)}{171}-93.78\)
\(=\dfrac{171\left(93^2-93.78+73^2\right)}{171}-93.78\)
\(=93^2-93.78+73^2-93.78\)
\(=93^2-2.93.78+73^2=\left(93-73\right)^2=20^2=400\)