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\(B=\left(\frac{x-2}{2x-2}-\frac{3}{2-2x}-\frac{x+3}{2x+2}\right):\left(1-\frac{x-3}{x+1}\right)\) \(ĐKXĐ:x\ne\pm1\)
\(B=\left(\frac{\left(x-2\right)\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}+\frac{3\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}-\frac{\left(x+3\right)\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}\right)\)\(:\left(\frac{x+1-x+3}{x+1}\right)\)
\(B=\left(\frac{x^2-x-2+3x+3-x^2-2x+3}{2\left(x-1\right)\left(x+1\right)}\right):\left(\frac{4}{x+1}\right)\)
\(B=\left(\frac{4}{2\left(x-1\right)\left(x+1\right)}\right):\left(\frac{4}{x+1}\right)\)
\(B=\frac{4}{2\left(x-1\right)\left(x+1\right)}.\frac{x+1}{4}=\frac{1}{2\left(x-1\right)}\)
\(\frac{3^2-1}{5^2-1}\times\frac{7^2-1}{9^2-1}\times\frac{11^2-1}{13^2-1}\times...\times\frac{43^2-1}{45^2-1}\)
\(=\frac{2\times4}{4\times6}\times\frac{6\times8}{8\times10}\times\frac{10\times12}{12\times14}\times...\times\frac{42\times44}{44\times46}\)
\(=\frac{2\times4\times6\times8\times...\times42\times44}{4\times6\times8\times10\times...\times44\times46}\)
\(=\frac{2}{46}=\frac{1}{23}\)
\(8x-x^2-22=-\left(x^2-8x+22\right)=-\left(x^2-2.x.4+4^2+6\right)=-\left(x-4\right)^2-6< 0\)
với mọi \(x\).
Trả lời:
E = 12 - 22 + 32 - 42 + 52 - 62 + ... + 20112 - 20122
= ( 12 - 22 ) + ( 32 - 42 ) + ( 52 - 62 ) + ... + ( 20112 - 20122 )
= ( 1 - 2 )( 1 + 2 ) + ( 3 - 4 )( 3 + 4 ) + ( 5 - 6 )( 5 + 6 ) + ... + ( 2011 - 2012 )( 2011 + 2012 )
= ( - 1 ).3 + ( - 1).7 + ( - 1 ).11 + ... + ( - 1 ).4023
= - 3 - 7 - 11 - ... - 4023
= - ( 3 + 7 + 11 + ... + 4023 )
= - [ ( 3 + 4023 ).1006 : 2 ] (1006 là số số hạng)
= - 2025078
Tính nhanh:E=1^2-2^2+3^2-4^2+5^2-6^2+...+2011^2-2012^2
= ( 1^2 - 2^2 ) + ( 3^2 - 4^2 ) + ......... ( 2011^2 - 2012^2
= -3 + -7 + ..... + 4023
= 2025078
A = (x2 + x)2 + 2(x2 + x) + 1
= (x2 + x + 1)2
B = (x - a)4 - (x + a)4
= [(x - a)2]2 - [(x + a)2]2
= [(x - a)2 - (x + a)2].[(x - a)2 + (x + a)2]
= (x2 - 2ax + a2 - x2 - 2ax - a2)(x2 - 2ax + a2 + x2 + 2ax + a2)
= -4ax(2x2 + 2a2)
= -8ax(x2 + a2)
C = (x2 - 10x + 25) - 4y2
= (x - 5)2 - (2y)2
= (x - 5 + 2y)(x - 5 - 2y)
D = x6 + 27 = (x2)3 + 33
= (x2 + 3)[x4 - 3x2 + 9)
\(A=\left(x^2+x\right)^2+2\left(x^2+x\right)+1=\left(x^2+x+1\right)^2\)
\(B=\left(x-a\right)^4-\left(x+a\right)^4=\left[\left(x-a\right)^2\right]^2-\left[\left(x+a\right)^2\right]^2\)
\(=\left[\left(x-a\right)^2-\left(x+a\right)^2\right]\left[\left(x-a\right)^2+\left(x+a\right)^2\right]\)
\(=\left(x-a-x-a\right)\left(x-a+x+a\right)\left(x^2-2xa+a^2+x^2+2ax+a^2\right)\)
\(=-2a.2x\left(2x^2+2a^2\right)=-8ax\left(x^2+a^2\right)\)
3. A = x3 - 64 - ( x3 - x2 + x - 1 ) = x3 - 64 - x3 + x2 - x + 1 = x2 - x - 63
B = x3 + 8 - ( x3 - 8 ) = x3 + 8 - x3 + 8 = 16
C = x3 - 3x2 + 3x - 1 - ( 4x2 - 1 ) = x3 - 3x2 + 3x - 1 - 4x2 + 1 = x3 - 7x2 + 3x
D = x( x2 - 25 ) - ( x3 + 1 ) = x3 - 25x - x3 - 1 = -25x - 1
4. a) x2 - 4x + 1 = 0 <=> ( x2 - 4x + 4 ) - 3 = 0 <=> ( x - 2 )2 - (√3)2 = 0
<=> ( x - 2 - √3 )( x - 2 + √3 ) = 0 <=> x = 2 ± √3
b) 9x2 - 6x - 8 = 0 <=> ( 9x2 - 6x + 1 ) - 9 = 0 <=> ( 3x - 1 )2 - 32 = 0
<=> ( 3x - 4 )( 3x + 2 ) = 0 <=> x = 4/3 hoặc x = -2/3
c) x3 - 3x2 + 3x + 7 = 0 <=> ( x3 - 3x2 + 3x - 1 ) + 8 = 0
<=> ( x - 1 )3 + 23 = 0 <=> ( x + 1 )( x2 - 4x + 7 ) = 0
<=> x + 1 = 0 <=> x = -1 ( vì x2 - 4x + 7 = ( x - 2 )2 + 3 > 0 )
a, ( 2x – 3 )2 + ( 1 – 2x )(1 + 2x ) = 4
\(=>4x^2-9+1-4x^2=4\)
\(=>8x^2+10=4\)
\(=>8x^2=-6\)
\(=>x=\orbr{\begin{cases}\frac{3}{4}\\-\frac{3}{4}\end{cases}}\)
Vậy (tự nhé)
Hok tốt~
Từ a + b + c = 0 => ( a + b + c )2 = 0
<=> a2 + b2 + c2 + 2ab + 2bc + 2ca = 0
<=> ab + bc + ca = -7
=> ( ab + bc + ca )2 = 49
<=> a2b2 + b2c2 + c2a2 + 2ab2c + 2bc2a + 2a2bc = 49
<=> a2b2 + b2c2 + c2a2 + 2abc( a + b + c ) = 49
<=> a2b2 + b2c2 + c2a2 = 49 ( vì a + b + c = 0 )
Từ a2 + b2 + c2 = 14 => ( a2 + b2 + c2 )2 = 196
<=> a4 + b4 + c4 + 2a2b2 + 2b2c2 + 2c2a2 = 196
<=> a4 + b4 + c4 = 98
giúp em ạ e cảm ơn
giúp mình vs
a) \(\left(a^2-4\right)\left(a^2+4\right)\)
\(=a^4-8\)
c) \(\left(a-b\right)\left(a+b\right)\left(a^2+b^2\right)\left(a^4+b^4\right)\)
=\(\left(a^2-b^2\right)\left(a^2+b^2\right)=a^4-b^4\)
d) \(\left(a-b+c\right)\left(a+b+c\right)\)
=\(a^2-\left(b+c\right)^2\)
e) \(\left(x+2-y\right)\left(x-2-y\right)\)
=\(x-\left(2-y\right)\)
mik lm tắt có gì sai cho mik xin lỗi
( a2 - 4 )( a2 + 4 ) = a4 - 16
( x3 - 3y )( x3 + 3y ) = x6 - 9y2
( a - b )( a + b )( a2 + b2 )( a4 + b4 ) = ( a2 - b2 )( a2 + b2 )( a4 + b4 ) = ( a4 - b4 )( a4 + b4 ) = a8 - b8
( a - b + c )( a + b + c ) = ( a + c )2 - b2 = a2 - b2 + c2 + 2ac
( x + 2 - y )( x - 2 - y ) = ( x - y )2 - 22 = x2 - 2xy + y2 - 4