a) 42 : 24 + 1/4 x 24 =
b) X2 x X/y : y =
c) X x ( X + 1 ) =
d) X2 x ( X + 1 ) - X3 =
e) X2 - X x ( X x 2 ) =
c) C = x(y2 +z2)+y(z2 +x2)+z(x2 +y2)+2xyz.
d) D = x3(y−z)+y3(z−x)+z3(x−y).
e) E = (x+y)(x2 −y2)+(y+z)(y2 −z2)+(z+x)(z2 −x2).
b) x2 +2x−24 = 0.
d) 3x(x+4)−x2 −4x = 0.
f) (x−1)(x−3)(x+5)(x+7)−297 = 0.
(2x−1)2 −(x+3)2 = 0.
c) x3 −x2 +x+3 = 0.
e) (x2 +x+1)(x2 +x)−2 = 0.
a) A = x2(y−2z)+y2(z−x)+2z2(x−y)+xyz.
b) B = x(y3 +z3)+y(z3 +x3)+z(x3 +y3)+xyz(x+y+z). c) C = x(y2 −z2)−y(z2 −x2)+z(x2 −y2).
Đề bài yêu cầu gì vậy em.
Bài 3: Giải phương trình:
a) x3+ 2x2 + x +2 = 0
b) x3 – x2 – 21x + 45 = 0
c) x3 + 3x2+4x + 2 = 0
d) x4+ x2 +6x – 8 = 0
e) (x2 + 1)2 = 4 ( 2x – 1 )
Bài 4: Giải phương trình:
a) ( x2-5x)2 + 10( x2 – 5x) + 24 = 0
b) ( x2 + 5x)2 - 2( x2 + 5x) = 24
c) ( x2 + x – 2)(x2 + x – 3) = 12
d) x ( x+1) (x2 + x + 1) = 42
Bài 1
a/ \(x\left(x^2+1\right)+2\left(x^2+1\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x^2+1\right)=0\Rightarrow x=-2\)
b/
\(\Leftrightarrow x^3-6x^2+9x+5x^2-30x+45=0\)
\(\Leftrightarrow x\left(x-3\right)^2+5\left(x-3\right)^2=0\)
\(\Leftrightarrow\left(x+5\right)\left(x-3\right)^2=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-5\\x=3\end{matrix}\right.\)
1.
c/ \(\Leftrightarrow x^3+2x^2+2x+x^2+2x+2=0\)
\(\Leftrightarrow x\left(x^2+2x+2\right)+x^2+2x+2=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2+2x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x^2+2x+2=0\left(vn\right)\end{matrix}\right.\)
d/
\(\Leftrightarrow x^4+x^3-2x^2-x^3-x^2+2x+4x^2+4x-8=0\)
\(\Leftrightarrow x^2\left(x^2+x-2\right)-x\left(x^2+x-2\right)+4\left(x^2+x-2\right)=0\)
\(\Leftrightarrow\left(x^2-x+4\right)\left(x^2+x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-x+4=0\left(vn\right)\\x^2+x-2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
Bài 1:
e/ \(\Leftrightarrow x^4+2x^2-8x+5=0\)
\(\Leftrightarrow x^4-2x^3+x^2+2x^3-4x^2+2x+5x^2-10x+5=0\)
\(\Leftrightarrow x^2\left(x-1\right)^2+2x\left(x-1\right)^2+5\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(x^2+2x+5\right)\left(x-1\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+2x+5=0\left(vn\right)\\x=1\end{matrix}\right.\)
Bài 2:
a/ Đặt \(x^2-5x=t\)
\(t^2+10t+24=0\Rightarrow\left[{}\begin{matrix}t=-4\\t=-6\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-5x=-4\\x^2-5x=-6\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-5x+4=0\\x^2-5x+6=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=1\\x=4\\x=2\\x=3\end{matrix}\right.\)
Phân tích đa thức thành nhân tử:
a) 25 y 2 + 10 y 8 +1;
b) ( x - 1 ) 4 - 2 ( x 2 - 2 x + 1 ) 2 +1;
c) (x + 1)(x + 2)(x + 3)(x + 4) - 24;
d) ( x 2 + 4 x + 8 ) 2 + 3 x ( x 2 + 4x + 8) + 2 x 2 ;
e) x 4 + 6 x 3 +7 x 2 -6x + 1.
Bài 1. Thực hiện phép tính:
a) 2xy(x2+ xy - 3y2)
b) (x + 2)(3x2 - 4x)
c) (x3 + 3x2 - 8x - 20) : (x + 2)
d) (x + y)2 + (x – y)2 – 2(x + y)(x - y) e) (a + b)3 - (a – b)3 – 2b3
f) 2x2(x – 2)+ 3x(x2 – x – 2) –5(3 – x2)
g) (x – 1)(x – 3) – (4 – x)(2x + 1) – 3x2 + 2x – 5
c: \(=\dfrac{x^3+2x^2+x^2+2x-10x-20}{x+2}\)
\(=x^2+x-10\)
Phân tích các đa thức sau thành nhân tử:
a) 8 x 3 - 2x; b) 5x - 25 x 2 + 10 x 3 9 ;
c) -5 x 3 (x + 1) + x + 1; d) x 3 27 + x 6 729 − x 9 ;
e) x ( y - x ) 2 - x 2 + 2xy - y 2 ; g) x ( x – y ) 2 - y ( x – y ) 2 + x y 2 - x 2 y.
a) 3x(x+1)-x(3x+2)
b) 2x(x2-5x+6)+(x-1)(x+3)
c) (x2-xy+y2)-(x2+2xy+y2)
d) (2/5xy+x-y)-(3x+4y)-2/5xy
e) 2xy(x2-4xy+4y2)
f) (x+y)(xy+5)
g) (x3-2x2-x+2):(x-1)
h) (2x2+3x-2):(2x-1)
Tính diện tích hình phẳng giới hạn bởi các đường sau:
a) y = 2x – x 2 , x + y = 2 ;
b) y = x 3 – 12x, y = x 2
c) x + y = 1, x + y = -1, x – y = 1, x – y = -1;
d)
e) y = x 3 – 1 và tiếp tuyến với y = x 3 – 1 tại điểm (-1; -2).
a) Đáp số: 1/6
b) Đáp số: 937/12.
Hướng dẫn:
c) Đáp số: 2
Hướng dẫn:
d) π/2 - 1
Hướng dẫn:
Đặt x = tan t để tính
e) Đáp số: 27/4
Hướng dẫn: Phương trình tiếp tuyến tại (-1; -2) là y = 3x + 1. Do đó, diện tích :
Phân tích các đa thức sau thành nhân tử :
a) 3x2 – 7x + 2;
b) a(x2 + 1) – x(a2 + 1).;
c)(x+2)(x+3)(x+4)(x+5)-24;
d)(a+1)(a+3)(a+5)(a+7)+15;
e)x2 + 2xy + 7x + 7y + y2 + 10
(x2 là x bình,y 2 là y bình,a2 là a bình nha)
Giúp mình với:33
a) 3x2 – 7x + 2
\(=3x^2-6x-x+2\)
\(=\left(3x^2-6x\right)-\left(x-2\right)\)
\(=3x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(3x-1\right)\)
b) a(x2 + 1) – x(a2 + 1)
\(=ax^2+a-\left(a^2x+x\right)\)
\(=a\left(x^2+1\right)-x\left(a^2+1\right)\)
.......?
a) Ta có: \(3x^2-7x+2\)
\(=3x^2-6x-x+2\)
\(=3x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(3x-1\right)\)
b) Ta có: \(a\left(x^2+1\right)-x\left(a^2+1\right)\)
\(=x^2a+a-a^2x-x\)
\(=\left(x^2a-a^2x\right)+\left(a-x\right)\)
\(=xa\left(x-a\right)-\left(x-a\right)\)
\(=\left(x-a\right)\left(xa-1\right)\)
c) Ta có: \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+120-24\)
\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+96\)
\(=\left(x^2+7x\right)^2+16\left(x^2+7x\right)+6\left(x^2+7x\right)+96\)
\(=\left(x^2+7x\right)\left(x^2+7x+16\right)+6\left(x^2+7x+16\right)\)
\(=\left(x^2+7x+16\right)\left(x^2+7x+6\right)\)
\(=\left(x^2+7x+16\right)\left(x+1\right)\left(x+6\right)\)
d) Ta có: \(\left(a+1\right)\left(a+3\right)\left(a+5\right)\left(a+7\right)+15\)
\(=\left(a^2+8a+7\right)\left(a^2+8a+15\right)+15\)
\(=\left(a^2+8a\right)^2+22\left(a^2+8a\right)+105+15\)
\(=\left(a^2+8a\right)^2+22\left(a^2+8a\right)+120\)
\(=\left(a^2+8a\right)^2+12\left(a^2+8a\right)+10\left(a^2+8a\right)+120\)
\(=\left(a^2+8a\right)\left(a^2+8a+12\right)+10\left(a^2+8a+12\right)\)
\(=\left(a^2+8a+12\right)\left(a^2+8a+10\right)\)
\(=\left(a+2\right)\left(a+6\right)\left(a^2+8a+10\right)\)
Phân tích các đa thức sau thành nhân tử:
a) x2 - 9 - x2 (x2 - 9) d) x2 + 5x + 6 h) a2 + b2 + 2a – 2b – 2ab
b) x2(x-y) + y2(y-x) e) 3x2 – 4x – 4 i) (x + 1)2 – 2(x + 1)(y – 3) + (y – 3)2
c) x3+27+(x+3)(x-9) g) x4 + 64y4 k) x2(x + 1) – 2x(x + 1) + x + 1
Mình đang cần gấp ạ
a: \(x^2-9-x^2\left(x^2-9\right)\)
\(=\left(x^2-9\right)-x^2\left(x^2-9\right)\)
\(=\left(x^2-9\right)\left(1-x^2\right)\)
\(=\left(1-x\right)\left(1+x\right)\left(x-3\right)\left(x+3\right)\)
b: \(x^2\left(x-y\right)+y^2\left(y-x\right)\)
\(=x^2\left(x-y\right)-y^2\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2-y^2\right)\)
\(=\left(x-y\right)\left(x-y\right)\left(x+y\right)=\left(x-y\right)^2\cdot\left(x+y\right)\)
c: \(x^3+27+\left(x+3\right)\left(x-9\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)\)
\(=\left(x+3\right)\left(x^2-3x+9+x-9\right)\)
\(=\left(x+3\right)\left(x^2-2x\right)=x\left(x-2\right)\left(x+3\right)\)
d: \(x^2+5x+6\)
\(=x^2+2x+3x+6\)
\(=x\left(x+2\right)+3\left(x+2\right)=\left(x+2\right)\left(x+3\right)\)
e: \(3x^2-4x-4\)
\(=3x^2-6x+2x-4\)
\(=3x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(3x+2\right)\)
g: \(x^4+64y^4\)
\(=x^4+16x^2y^2+64y^4-16x^2y^2\)
\(=\left(x^2+8y^2\right)^2-\left(4xy\right)^2\)
\(=\left(x^2+8y^2-4xy\right)\left(x^2+8y^2+4xy\right)\)
h: \(a^2+b^2+2a-2b-2ab\)
\(=a^2-2ab+b^2+2a-2b\)
\(=\left(a-b\right)^2+2\left(a-b\right)=\left(a-b\right)\left(a-b+2\right)\)
i: \(\left(x+1\right)^2-2\left(x+1\right)\left(y-3\right)+\left(y-3\right)^2\)
\(=\left(x+1-y+3\right)^2\)
\(=\left(x-y+4\right)^2\)
k: \(x^2\left(x+1\right)-2x\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-2x+1\right)\)
\(=\left(x+1\right)\left(x-1\right)^2\)
a) (2x+1)2+(2x+3)2-2(2x+1)(2x+3)
b) (2x-3)(2x+3)-(x-+5)2-(x-1)(x+2)
c) (24x2y3z2-12x3y2z3+36x2y2z2):(-6x2y2z2)
d) (x+2y)(x2-2xy+4y2)-(x-y)(x2+xy+y2)
e) (x3+4x2-x-4):(x+4)
f) x2(x+y)+y2(x+y)+2x2y+2xy2
g) (x+y)2+(x-y)2-2(x+y)(x-y)
h) (a+b)2-(a-b)3-2b3
i) (x-y)(x+y)(x2+y2)(x4+y4)
Mong mọi người giúp đỡ vì mai em phải nộp