2x2xy:3+3xy:2+y=575
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![](https://rs.olm.vn/images/avt/0.png?1311)
A=x^3 + y^3 + 3xy(x+y)
=x+3x^y+3xy^2+y^3
=(x+y)^3=2^3=8
B=x^2+2xy+y^2+4
=(x+y)^2+4=4+4=8
C=x^3+y^3+3xy(x+y)+7(x+y)
=(x+y)^3+7(x+y)
=2^3+7.2
=8+14=22
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 1: Ta có: A = \(x^3+y^3+3xy=x^3+y^3+3xy\times1=x^3+y^3+3xy\left(x+y\right)\)
\(=\left(x+y\right)^3=1^3=1\)
Câu 2: Ta có: \(B=x^3-y^3-3xy=\left(x-y\right)\left(x^2+xy+y^2\right)-3xy\)
\(=x^2+xy+y^2-3xy=x^2-2xy+y^2=\left(x-y\right)^2=1^2=1\)
Câu 3: Ta có: \(C=x^3+y^3+3xy\left(x^2+y^2\right)-6x^2.y^2\left(x+y\right)\)
\(=x^3+y^3+3xy\left(x^2+2xy+y^2-2xy\right)+6x^2y^2\)
\(=x^3+y^3+3xy\left(x+y\right)^2-3xy.2xy+6x^2y^2\)
\(=x^3+y^3+3xy.1-6x^2y^2+6x^2y^3\)
\(=x^3+y^3+3xy\left(x+y\right)=\left(x+y\right)^3=1^3=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu a) sai đề em ơi
Đề đúng là: x2 + y2 = (x + y)2 - 2xy
Giải theo đúng đề nè:
a) x2 + y2
= x2 + y2 + 2xy - 2xy
= (x + y)2 - 2xy
b) Đề cũng sai. Đề đúng phải là: x3 + y3 = (x + y)3 - 3xy(x + y)
Giải đề đúng là:
x3 + y3 = x3 + y3 + 3x2y + 3xy2 - 3x2y - 3xy2
= (x + y)3 - 3xy(x + y)
c) x3 - y3 = x3 - 3x2y + 3xy2 - y3 + 3x2y - 3xy2
= (x - y)3 + 3xy(x - y)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(575-\left(2x+70\right)=445\)
=>\(2x+70=575-445=130\)
=>\(2x=130-70=60\)
=>x=60/2=30
b: \(575-2\left(x+70\right)=445\)
=>\(2\left(x+70\right)=575-445=130\)
=>x+70=130/2=65
=>x=65-70=-5
c: \(x^5=32\)
=>\(x^5=2^5\)
=>x=2
d: \(\left(3x-1\right)^3=8\)
=>\(\left(3x-1\right)^3=2^3\)
=>3x-1=2
=>3x=3
=>\(x=\dfrac{3}{3}=1\)
e: \(\left(x-2\right)^3=27\)
=>\(\left(x-2\right)^3=3^3\)
=>x-2=3
=>x=5
f: \(\left(2x-3\right)^2=9\)
=>\(\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)
g: \(2x+5=3^4:3^2\)
=>\(2x+5=3^2\)
=>2x+5=9
=>2x=9-5=4
=>x=4/2=2
h: \(\left(4x-5^2\right)\cdot7^3=7^4\)
=>\(4x-25=\dfrac{7^4}{7^3}=7\)
=>4x=25+7=32
=>\(x=\dfrac{32}{4}=8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(A=x\left(x+2\right)+y\left(y-2\right)-2xy+37\)
\(A=x^2+2x+y^2-2y-2xy+37\)
\(A=\left(x^2-2xy+y^2\right)+\left(2x-2y\right)+37\)
\(A=\left(x-y\right)^2+2\left(x-y\right)+37\)
\(A=\left(x-y\right)^2+2\left(x-y\right)+1+36\)
\(A=\left(x-y+1\right)^2+36\)
Thay x - y = 7 vào A
\(A=\left(7+1\right)^2+36\)
\(A=8^2+36\)
\(A=64+36\)
\(A=100\)
b) \(B=x^3+x^2-y^3+y^2+xy-3x^2y+3xy^2-3xy-9\)
\(B=\left(x^3-3x^2y+3xy^2-y^3\right)+\left(x^2+xy-3xy+y^2\right)-9\)
\(B=\left(x-y\right)^3+\left(x^2-2xy+y^2\right)-9\)
\(B=\left(x-y\right)^3+\left(x-y\right)^2-9\)
Thay x - y = 7 vào B
\(B=7^3+7^2-9\)
\(B=343+49-9\)
\(B=383\)
c) \(C=x^3-x^2-y^3-y^2-3xy\left(x-y\right)+2xy\)
\(C=\left[x^3-y^3-3xy\left(x-y\right)\right]-\left(x^2-2xy+y^2\right)\)
\(C=\left(x-y\right)^3-\left(x-y\right)^2\)
Thay x - y = 7 vào C
\(C=7^3-7^2\)
\(C=343-49\)
\(C=294\)
d) \(D=x^2\left(x+1\right)-y^2\left(y-1\right)+xy-3xy\left(x-y+1\right)-95\)
\(D=x^3+x^2-y^3+y^2+xy-3x^2y+3xy^2-3xy-95\)
\(D=\left(x^3-3x^2y+3xy^2-y^3\right)+\left(x^2-2xy+y^2\right)-95\)
\(D=\left(x-y\right)^3+\left(x-y\right)^2-95\)
Thay x - y = 7 vào D
\(D=7^3+7^2-95\)
\(D=343+49-95\)
\(D=297\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(-\dfrac{2}{3}\left(x^2y^2\right)^2+\dfrac{1}{3}xy^2\cdot0,75x-3xy\cdot\left(-2x\right)\)
\(=-\dfrac{2}{3}x^4y^4+\dfrac{1}{3}xy^2\cdot\dfrac{3}{4}x-3xy\cdot\left(-2x\right)\)
\(=-\dfrac{2}{3}x^4y^4+\left(\dfrac{1}{3}\cdot\dfrac{3}{4}\right)\left(x\cdot x\right)y^2-\left(3\cdot-2\right)\left(x\cdot x\right)y\)
\(=-\dfrac{2}{3}x^4y^4+\dfrac{1}{4}x^2y^2+6x^2y\)
2 x 2 x y : 3 + 3 x y : 2 + y = 575
=>\(\frac{4y}{3}+\frac{3y}{2}+y=575\)
=> \(\frac{8y+9y+6y}{6}=575\)
\(\Rightarrow\frac{23}{6}y=575\)
\(\Rightarrow y=575\div\frac{23}{6}=575\cdot\frac{6}{23}=150\)
Vậy y = 150