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29 tháng 10 2017
1,Thực hiện phép tính :
a, (x + 2)9 : (x + 2)6
=(x+2)9-6
=(x+2)3
b, (x - y) 4 : (x - 2)3
=(x-y)4-3
=x-y
c, ( x2+ 2x + 4)5 : (x2 + 2x + 4)
=(x2+2x+4)5-1
=(x2+2x+4)4
d, 2(x2 + 1)3 : 1/3(x2 + 1)
=(2÷1/3).[(x2+1)3÷(x2+1)]
=6(x2+1)2
e, 5 (x - y)5 : 5/6 (x - y)2
=(5÷5/6).[(x-y)5÷(x-y)2]
=6(x-y))3
3 tháng 9 2016
a/ \(2^{x+1}.3y=12^x\Leftrightarrow2^x.2.3y=2^x.2^x.3^x\Leftrightarrow2^{x-1}.3^{x-1}=y\Leftrightarrow y=6^{x-1}\)
Vậy \(\left(x;y\right)=\left(x;6^{x-1}\right)\)
b/ \(10^x:5^y=20^y\Leftrightarrow10^x=20^y.5^y\Leftrightarrow10^x=100^y\Leftrightarrow10^x=10^{2y}\Leftrightarrow x=2y\)
Vậy \(\left(x;y\right)=\left(2y;y\right)\)
3 tháng 9 2016
c/ Ta có : \(2^x=4^{y-1}\Leftrightarrow2^x=2^{2y-2}\Leftrightarrow x=2y-2\)
Lại có : \(27y=3^{x+8}\Leftrightarrow27y=3^{x+5}.27\Leftrightarrow y=3^{x+5}\)
Suy ra hệ : \(\begin{cases}x=2y-2\\y=3^{x+5}\end{cases}\)
7 tháng 9 2022
a: \(=\dfrac{5}{2}x-2x+\dfrac{7}{2}=\dfrac{1}{2}x+\dfrac{7}{2}\)
b: \(=\dfrac{-1}{4}x^4-3x^2+\dfrac{9}{4}x\)
c: \(=\dfrac{1}{5}x+\dfrac{1}{15}xy+\dfrac{7}{10}x^2\)
d: \(=-9x^3-1-12y+27xy\)
13 tháng 11 2017
Bài 2 .
a) \(\dfrac{2x}{x^2+2xy}+\dfrac{y}{xy-2y^2}+\dfrac{4}{x^2-4y^2}\)
\(=\dfrac{2x}{x\left(x+2y\right)}+\dfrac{y}{y\left(x-2y\right)}+\dfrac{4}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\dfrac{2xy\left(x-2y\right)+xy\left(x+2y\right)+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)
\(=\dfrac{2x^2y-2xy^2+x^2y+2xy^2+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)
\(=\dfrac{3x^2y+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)
b) Sai đề hay sao ý
c) \(\dfrac{2x+y}{2x^2-xy}+\dfrac{16x}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)
\(=\dfrac{2x+y}{x\left(2x-y\right)}+\dfrac{-16x}{\left(2x-y\right)\left(2x+y\right)}+\dfrac{2x-y}{x\left(2x+y\right)}\)
\(=\dfrac{\left(2x+y\right)^2-16x^2+\left(2x-y\right)^2}{x\left(2x-y\right)\left(2x+y\right)}\)
\(=\dfrac{4x^2+4xy+y^2-16x^2+4x^2-4xy+y^2}{x\left(2x-y\right)\left(2x+y\right)}\)
\(=\dfrac{-8x^2}{x\left(2x-y\right)\left(2x+y\right)}\)
d) \(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{2}{1-x^2}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{4}{1-x^4}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
.....
\(=\dfrac{16}{1-x^{16}}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{32}{1-x^{32}}\)
LD
21 tháng 8 2018
a,
\(x^2+y^2=\left(x+y\right)^2-2xy=1^2-2\cdot\left(-6\right)=1-\left(-12\right)=13\)
\(x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)=1\cdot\left[13-\left(-6\right)\right]=19\)
\(x^5+y^5=\left(x+y\right)\left(x^2+y^2\right)^2-\left(2x^3y^2+xy^4+x^4y+2x^2y^3\right)=169-\left[2\left(xy\right)^2\left(x+y\right)+xy\left(x^3+y^3\right)\right]=169-\left[2\cdot36\cdot1-6\cdot19\right]=211\)
Y
8 tháng 8 2018
a) \(2x+2y\)
\(=2\left(x+y\right)\)
b) \(5x+20y\)
\(=5\left(x+4y\right)\)
c) \(6xy-30y\)
\(=6y\left(x-5\right)\)
d) \(5x\left[x-110-10y\left(x-11\right)\right]\)
\(=5x\left(x-110-10xy+110\right)\)
\(=5x\left(x-10xy\right)\)
\(=5x^2\left(1-10y\right)\)
e) \(x^3-4x^2+x\)
\(=x\left(x^2-4x+1\right)\)
f) \(x\left(x+y\right)-\left(2x+2y\right)\)
\(=x\left(x+y\right)-2\left(x+y\right)\)
\(=\left(x+y\right)\left(x-2\right)\)
h) \(5x\left(x-2y\right)+2\left(2y-x\right)\)
\(=5x\left(x-2y\right)-2\left(x-2y\right)\)
\(=\left(x-2y\right)\left(5x-2\right)\)
i) \(x^2y^3-\dfrac{1}{2}x^4y^8\)
\(=x^2y^3\left(1-\dfrac{1}{2}xy^5\right)\)
j) \(a^2b^4+a^3b-abc\)
\(=ab\left(ab^3+a^2-c\right)\)