CMR:
a,1 + 3 + 5 +......+ ( 2n - 1 ) = n2
b,1 x 4 + 2 x 7 + .............. + n x ( 3n + 1 )2 =n x ( n + 1 ) x ( 2n + 1 )
a)2x^2+3.(x-1).(x+1)-5x.(x+1)
b) (8-5x).(x+2)+4.(x-2).(x+1)+2.(x-2).(x+2)+10
c) 4.(x-1).(x+5)-(x+2).(x+5)-3.(x-1).(x+2)
d) (x^2n+x^n y^n +y^2n).(x^n-y^n).(x^3n+y^3n)
GIÚP MÌNH VỚI Ạ
1.Tìm x:
a) -13(x-1)+3(2-x)=6
b)7.(x-3)-3x(3-x)=0
c)2|3x-1|-5=7
2.Tìm n để:
a) (3n-2) chia hết cho (n-1)
b) (4-2n) chia hết cho ( 2n+3)
1.Tìm x:
a) -13(x-1)+3(2-x)=6
-13x-x+6-3x=6
x-x-3x=6+13-6
5x=13
x=13/5
vậy x=13/5
b)7.(x-3)-3(3-x)=0
7x-21-9-3x=0
7x-3x=0+21+9
4x=30
x=15/2
vậy x=15/2
c)2|3x-1|-5=7
2|3x-1|=7+5
2|3x-1|=12
|3x-1|=12:2
|3x-1|=6
* 3x-1=6 * 3x-1=-6
3x=6+1 3x=-6+1
3x=7 3x=-5
x=7/3 x=-5/3
vậy x=7/3 hoặc x=-5/3
a) 2x^2 +3 × ( x - 1)×(x+1)-5x × (x+1)
b) (8-5x)×(x+2)+4× (x-2) × (x +1)+2 × ( x -2)×( x+2)+10
c) 4 × ( x-1) × ( x-5)-( x-2)×( x+5)-3× ( x-1)×( x+2)
d) (x2n + xn yn + y2n)×( xn - yn ) × ( x3n + y3n)
1. Thực hiện phép tính :
a) ( 8 - 5x )( x + 2 ) + 4( x - 2 )( x + 1 ) + 2( x - 2 )( x + 2 ) + 10
b) 4( x - 1 )( x + 5 ) - ( x + 2 )( x + 5 ) - 3( x - 1 )( x + 2 )
c) ( x2n + xnyn + y2n )( xn - yn )( x3n + y3n )
Bài làm :
\(a,\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)+10\)
\(=8x+16-5x^2-10x+\left(4x-8\right)\left(x+1\right)+2\left(x^2-2^2\right)+10\)
\(=8x+16-5x^2-10x+4x^2+4x-8x-8+2x^2-8+10\)
\(=\left(8x-10x+4x-8x\right)+\left(-5x^2+4x^2+2x^2\right)+\left(16-8-8+10\right)\)
\(=-6x+x^2+10\)
a)\(\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)+10\)\(=8x+16-5x^2-2+4x-8x-8+2x-4x-4+10\)\(=\left(8x+4x-8x+2x-4x\right)+\left(16-2-8-4+10\right)+5x^2\)
\(=2x+12+5x^2\)
b)\(4\left(x-1\right)\left(x+5\right)-\left(x+2\right)\left(x+5\right)-3\left(x-1\right)\left(x+2\right)\)
\(=4x-4x-20-\left[x^2+5x+2x+10\right]-3\left[x^2+2x-1x-2\right]\)
\(=4x-4x-20-x^2-5x-2x-10-3x^2-6x+3x+6\)
\(=\left(4x-4x-5x-2x-6x+3x\right)+\left(-20-10+6\right)+\left(-x^2-3x^2\right)\)
\(=-10x-24-4x^2\)
c)\(\left(x^{2n}+x^ny^n+y^{2n}\right)\left(x^n-y^n\right)\left(x^{3n}+y^{3n}\right)\)
Xét tích \(\left(x^{2n}+x^ny^n+y^{2n}\right)\left(x^n-y^n\right)\Leftrightarrow\left(x^n\right)^3-\left(y^n\right)^3=x^{3n}-y^{3n}\)
Thay vào bt đã cho ta có \(\left(x^{3n}-y^{3n}\right)\left(x^{3n}+y^{3n}\right)\)
\(\Leftrightarrow\left(x^{3n}\right)^2-\left(y^{3n}\right)^2=x^{6n}-y^{6n}\)
a) ( 8 - 5x )( x + 2 ) + 4( x - 2 )( x + 1 ) + 2( x - 2 )( x + 2 ) + 10
= -2x - 5x2 + 16 + 4( x2 - x - 2 ) + 2( x2 - 4 ) + 10
= -2x - 5x2 + 16 + 4x2 - 4x - 8 + 2x2 - 8 + 10
= x2 - 6x + 10
b) 4( x - 1 )( x + 5 ) - ( x + 2 )( x + 5 ) - 3( x - 1 )( x + 2 )
= 4( x2 + 4x - 5 ) - ( x2 + 7x + 10 ) - 3( x2 + x - 2 )
= 4x2 + 16x - 20 - x2 - 7x - 10 - 3x2 - 3x + 6
= 6x - 24 = 6( x - 4 )
c) ( x2n + xnyn + y2n )( xn - yn )( x3n + y3n )
= [ ( xn )3 - ( yn )3 ]( x3n + y3n )
= ( x3n - y3n )( x3n + y3n )
= ( x3n )2 - ( y3n )2 = x6n - y6n
Bài 1: Tính:
a, 4(x - 1 )(x + 5 ) - (x + 2 )(x + 5 ) - 3(x - 1)(x + 2 )
b, ( x2n + xnyn + y2n )( xn - yn )( x3n + y3n )
Bài 2: Tìm x :
a, ( 2x + 3 )( x - 4 ) + ( x - 5 )( x - 2 ) = ( 3x - 5 )( x - 4 )
b, ( 8x - 3 )( 3x + 2 ) - ( 4x + 7 )( x + 4 ) = ( 2x +1 )( 5x - 1) - 33
Help me!!! Các pạn có thể áp dụng các hằng đẳng thức nha, chú ý đến cả dấu nha!!!
Mk lm câu b bài 2 há!
b, ( 8x - 3 )( 3x + 2 ) - ( 4x + 7 )( x + 4 ) = ( 2x +1 )( 5x - 1) =- 33
Pt <=> 3x ( 8x - 3 ) + 2( 8x- 33) - ( x ( 4x + 7) ) + ( 2x + 1) - 5x ( 2x + 1) + 33 = 0
<=> 24x2 - 9x + 16x - 6 - ( 4x2 + 7x + 16x + 28) + 2x + 1 - 10x2 - 5x + 33 = 0
<=> 24x2 - 9x + 16x - 6 - 4x2 - 7x - 16x - 28 + 2x + 1 - 10x2 - 19x = 0 <=> x ( 10x - 19) = 0
=> \(\orbr{\begin{cases}x=0\\10x-19=0\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=0\\x=\frac{19}{10}\end{cases}}\)
^^ Ok con tê tê!
Các bạn ơi giúp mình nhé! Mình cần gấp lắm ạ! Cảm ơn nhiều ạ!!!!!!!! Bài 1: Thực hiện phép tính a, 2x^2 +3(x-1)(x+1)-5x(x+1)
b, (8-5x)(x+2)+4(x-2)(x+1)+2(x-2)(x+2)+10
c, 4(x-1)(x+5)-(x+2)(x+5)-3(x-1)(x+2)
d, (x^2n + x^n.y^n+y^2n)(x^n-y^n)(x^3n+y^3n)
Bài 2: Tìm x
a, (x+2)(x+3)-(x-2)(x+5)=0
b, (2x+3)(x-4)+(x-5)(x-2)=(3x-5)(x-4)
c, (8-5x)(x+2)+4(x-2)(x+1)+2(x-2)(x+2)=0
d, (8x-3)(3x+2)-(4x+7)(x+4)= (2x+1)(5x-1)-33
Các cậu ơi tớ cần rất gấp ạ, mong mọi người giúp đỡ owo
Bài 1:
a) (3-2x)(x-2)+4(x-1)(x-3)-2(x-2)(x+2)
b) (xn+yn)(x2n-xn.yn+y2n)(x3n—y3n) (n thuộc N)
c) (x-3)(x+7)-(2x-5)(x+1)
d) (x+8)2–2(x+8)(x–2)+(x–2)2
Bài 2:
a)(3x^n + 1 - 2x^n )4x^2
b) 2(x^2n + 2xnyn+y^2n)-y^n(4x^n+2y^n)
c)(x^2n+xnyn+y^2n)(x^n-y^n)(x^3n+y^3n)
d)4^n+1 - 3.4^n
a: \(4x^2\left(3x^{n+1}-2x^n\right)\)
\(=4x^2\cdot3x^{n+1}-4x^2\cdot2x^n\)
\(=12x^{n+3}-8x^{n+2}\)
b: \(2\left(x^{2n}+2x^ny^n+y^{2n}\right)-y^n\left(4x^n+2y^n\right)\)
\(=2x^{2n}+4x^ny^n+2y^{2n}-4x^ny^n-2y^{2n}\)
\(=2x^{2n}\)
c: \(=\left(x^{3n}-y^{3n}\right)\left(x^{3n}+y^{3n}\right)\)
\(=x^{6n}-y^{6n}\)
d: \(=4^n\cdot4-3\cdot4^n=4^n\)
a: 4x2(3xn+1−2xn)4x2(3xn+1−2xn)
=4x2⋅3xn+1−4x2⋅2xn=4x2⋅3xn+1−4x2⋅2xn
=12xn+3−8xn+2=12xn+3−8xn+2
b: 2(x2n+2xnyn+y2n)−yn(4xn+2yn)2(x2n+2xnyn+y2n)−yn(4xn+2yn)
=2x2n+4xnyn+2y2n−4xnyn−2y2n=2x2n+4xnyn+2y2n−4xnyn−2y2n
=2x2n=2x2n
c: =(x3n−y3n)(x3n+y3n)=(x3n−y3n)(x3n+y3n)
=x6n−y6n=x6n−y6n
d: =4n⋅4−3⋅4n=4n
TÌM X ∈ N BIẾT :
1) 6⋮(N+2)
2) 11⋮(2N-1)
3) 13⋮(N-1)
4) 23⋮(2N-1)
5) 24⋮(N+3)
6) (N+7)⋮(N+2)
7) (2N+8)⋮(2N+1)
8) (2N+9)⋮(2N-1)
9) (3N+7)⋮(N+1)
10) (2N+10)⋮(N+2)