cm 2/xy:(1/x-1/y)2-x2+y/(x-y)2=-1
Những câu hỏi liên quan
rút gọn P=2/x-(x2/(x2-xy)+(x2-y2)/xy-y2/(y2-xy)):(x2-xy+y2)/(x-y)
r tìm gt P với |2x-1|=1 ; |y+1|=1/2
Bạn cần viết đề bằng công thức toán để được hỗ trợ tốt hơn.
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a) -(x-y)(x2+xy-1)
b) x2(x-1)-(x2+1)(x-y)
c) (3x-2)(2x-1)+(-5x-1)(3x+2)
d) (3x-5)(2x+11)-(2x3)(3x+7)
Bài 2: Tính giá trị biểu thức
C=x(x2-y)-x2(x+y)+y(x2-x) tại x=1/2, y=-1
a)-(x-y)(x2+xy-1)=-(x3+x2y-x-x2y-xy2+y)
=-(x3-xy2-x+y)
=-x3+xy2+x-y
b)x2(x-1)-(x3+1)(x-y)=x3-x2-x3+x2y-x+y
=-x2+x2y-x+y
c)(3x-2)(2x-1)+(-5x-1)(3x+2)=6x2-3x-4x+2-15x2-10x-3x-2
=-9x2-20x
d) hình như bạn ghi lỗi
Bài 2: C=x(x2-y)-x2(x+y)+y(x2-x)
=x3-xy-x3-x2y+x2y-xy
=-2xy
Thay x=1/2,y=-1 vào C, ta có:
C=-2.1/2.(-1)=1
Vậy C=1 khi x=1/2 và y=-1.
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Thực hiện phép tính
a) x. (x + y) + 5y - x2
b) (x - 2). (y + 1) - xy + 4
c) (4x2y + 12xy2 - 8xy) : (2xy)
d) (x - 4)2 - 7 + 8x
Bài 6. Cho x2 + xy = 3
Tính giá trị biểu thức M = x(x2 + y) + x2(y + 1) - 3(x + 1)
Bài 1:
a: \(x\left(x+y\right)+5y-x^2\)
\(=x^2+xy+5y-x^2\)
=xy+5y
b: \(\left(x-2\right)\left(y+1\right)-xy+4\)
\(=xy+x-2y-2-xy+4\)
=-2y+x+2
c: \(\dfrac{\left(4x^2y+12xy^2-8xy\right)}{2xy}\)
\(=\dfrac{2xy\cdot2x+2xy\cdot6y-2xy\cdot4}{2xy}\)
=2x+6y-4
d: \(\left(x-4\right)^2+8x-7\)
\(=x^2-8x+16+8x-7\)
\(=x^2+9\)
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1.
a.(-xy)(-2x2y+3xy-7x)
b.(1/6x2y2)(-0,3x2y-0,4xy+1)
c.(x+y)(x2+2xy+y2)
d.(x-y)(x2-2xy+y2)
2.
a.(x-y)(x2+xy+y2)
b.(x+y)(x2-xy+y2)
c.(4x-1)(6y+1)-3x(8y+4/3)
1.
\(a,\left(-xy\right)\left(-2x^2y+3xy-7x\right)\)
\(=2x^3y^2-3x^2y^2+7x^2y\)
\(b,\left(\dfrac{1}{6}x^2y^2\right)\left(-0,3x^2y-0,4xy+1\right)\)
\(=-\dfrac{1}{20}x^4y^3-\dfrac{1}{15}x^3y^3+\dfrac{1}{6}x^2y^2\)
\(c,\left(x+y\right)\left(x^2+2xy+y^2\right)\)
\(=\left(x+y\right)^3\)
\(=x^3+3x^2y+3xy^2+y^3\)
\(d,\left(x-y\right)\left(x^2-2xy+y^2\right)\)
\(=\left(x-y\right)^3\)
\(=x^3-3x^2y+3xy^2-y^3\)
2.
\(a,\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(=x^3-y^3\)
\(b,\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(=x^3+y^3\)
\(c,\left(4x-1\right)\left(6y+1\right)-3x\left(8y+\dfrac{4}{3}\right)\)
\(=24xy+4x-6y-1-24xy-4x\)
\(=\left(24xy-24xy\right)+\left(4x-4x\right)-6y-1\)
\(=-6y-1\)
#Toru
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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)
Cho (x+y-1)2 = xy tìm GTNN của P=1/xy + 1/x2+y2 + √xy/x+y
17 tháng 10 2023 lúc 19:05
Cho \(x>0;\) \(y>0;\) \(x+y\le1\). CM: \(\dfrac{1}{x^2+xy}+\dfrac{1}{y^2+xy}\ge4\)
\(VT\ge\dfrac{4}{x^2+y^2+2xy}=\dfrac{4}{\left(x+y\right)^2}\ge4\) (vì \(x+y\le1\) )
Dấu "=" xảy ra \(\Leftrightarrow x=y=\dfrac{1}{2}\)
Ta có đpcm
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Tính:
a,2x(x - 1) - 3(x2 + 4x) + x(x + 2)
b,(2x - 3) (3x + 5) - (x - 1) (6x + 2) + 3 - 5x
c,(x - y)(x2 + xy + y2) - (x + y)(x2- y2)
\(a.2x\left(x-1\right)-3\left(x^2+4x\right)+x\left(x+2\right)\)
\(=2x^2-2x-3x^2-12x+x^2+2x\)
\(=-12x\)
\(b.\left(2x-3\right)\left(3x+5\right)-\left(x-1\right)\left(6x+2\right)+3-5x\)
\(=6x+10x-9x^2-15-6x^2-2x-6x-2+3-5x\)
\(=-15x^2+3x-14\)
\(c.\left(x-y\right)\left(x^2+xy+y^2\right)-\left(x+y\right)\left(x^2-y^2\right)\)
\(=x^3-y^3-x^3+y^3+x^2y-y^3\)
\(=y^3+x^2y\)
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6). – x2 y(xy2 – 1/2 xy + 3/4 x2 y2 )7). (3xy – x2 + y). 2/3 x2 y8). (4x3 – 5xy + 2x)( – 1/2 xy)9). 2x2 (x2 + 3x + 1/2 )10). – 3/2 x4 y2 (6x4 − 10/9 x2 y3 – y5 )11). 2 3 x3 (x + x2 – 3/4 x5 )12). 2xy2 (xy + 3x2 y – 2/3 xy3 )13). 3x(2x3 – 1/3 x2 – 4x)14). 3/5 x3 y5 (7x4 + 5x2 y − 10/21 x4 y3 –y4 )
Đọc tiếp
6). – x2 y(xy2 – 1/2 xy + 3/4 x2 y2 )
7). (3xy – x2 + y). 2/3 x2 y
8). (4x3 – 5xy + 2x)( – 1/2 xy)
9). 2x2 (x2 + 3x + 1/2 )
10). – 3/2 x4 y2 (6x4 − 10/9 x2 y3 – y5 )
11). 2 3 x3 (x + x2 – 3/4 x5 )
12). 2xy2 (xy + 3x2 y – 2/3 xy3 )
13). 3x(2x3 – 1/3 x2 – 4x)
14). 3/5 x3 y5 (7x4 + 5x2 y − 10/21 x4 y3 –y4 )
6: \(-x^2y\left(xy^2-\dfrac{1}{2}xy+\dfrac{3}{4}x^2y^2\right)\)
\(=-x^3y^3+\dfrac{1}{2}x^3y^2-\dfrac{3}{4}x^4y^3\)
7: \(\dfrac{2}{3}x^2y\cdot\left(3xy-x^2+y\right)\)
\(=2x^3y^2-\dfrac{2}{3}x^4y+\dfrac{2}{3}x^2y^2\)
8: \(-\dfrac{1}{2}xy\left(4x^3-5xy+2x\right)\)
\(=-2x^4y+\dfrac{5}{2}x^2y^2-x^2y\)
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9: \(2x^2\left(x^2+3x+\dfrac{1}{2}\right)=2x^4+6x^3+x^2\)
10: \(-\dfrac{3}{2}x^4y^2\left(6x^4-\dfrac{10}{9}x^2y^3-y^5\right)\)
\(=-9x^8y^2+\dfrac{5}{3}x^6y^5+\dfrac{3}{2}x^4y^7\)
11: \(\dfrac{2}{3}x^3\left(x+x^2-\dfrac{3}{4}x^5\right)=\dfrac{2}{3}x^3+\dfrac{2}{3}x^5-\dfrac{1}{2}x^8\)
12: \(2xy^2\left(xy+3x^2y-\dfrac{2}{3}xy^3\right)=2x^2y^3+6x^3y^3-\dfrac{4}{3}x^2y^5\)
13: \(3x\left(2x^3-\dfrac{1}{3}x^2-4x\right)=6x^4-x^3-12x^2\)
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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: \(=\dfrac{x^3+2x^2+x^2+2x-10x-20}{x+2}\)
\(=x^2+x-10\)
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