vay hoi gi

\(B=2x^4-y^4+x^2y^2+3y^2\\ =\left(x^4-y^4\right)+\left(x^4+x^2y^2\right)+3y^2\\ =\left(x^2-y^2\right)\left(x^2+y^2\right)+x^2\left(x^2+y^2\right)+3y^2\\ =x^2-y^2+x^2+3y^2\\ =2x^2+2y^2\\ =2\left(x^2+y^2\right)\\ =2\)

\(\left(a+b\right)^3-3ab\left(a+b\right)\\ =\left(a^3+3a^2b+3ab^2+b^3\right)-3a^2b-3ab^2\\ =a^3+b^3\)

b.

\(a^3+b^3+c^3-3abc\\ =\left(a+b\right)^3+c^3-3ab\left(a+b\right)-3abc\\ =\left(a+b+c\right)\left(\left(a+b\right)^2-\left(a+b\right)c+c^2\right)-3ab\left(a+b+c\right)\\ =\left(a+b+c\right)\left(a^2+2ab+b^2-ab-bc+c^2\right)-3ab\left(a+b+c\right)\\ =\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)\)

3.

\(2^x=256+2^y\\ \Rightarrow2^x-2^y=256\\ \Rightarrow2^y\left(2^{x-y}-1\right)=2^8\)

\(\Rightarrow2^y;2^{x-y}-1\in U\left(2^8\right)\)

Mà \(2^{x-y}-1\) là số lẻ

\(\Rightarrow2^{x-y}-1=1\\ \Rightarrow\left\{{}\begin{matrix}2^y=2^8\\2^{x-y}=2\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}y=8\\x-y=1\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}y=8\\x=9\end{matrix}\right.\)

4.

Gọi d là ƯCLN(2n+5;3n+7)

\(\Rightarrow\left\{{}\begin{matrix}2n+5⋮d\\3n+7⋮d\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}3\left(2n+5\right)⋮d\\2\left(3n+7\right)⋮d\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}6n+15⋮d\\6n+14⋮d\end{matrix}\right.\\ \Rightarrow\left(6n+15\right)-\left(6n+14\right)⋮d\\ \Rightarrow1⋮d\\ \Rightarrow d=1\)

=> đpcm

\(\left|x-5\right|+\left|x-1\right|\\ =\left|5-x\right|+\left|x-1\right|\\ \ge\left|5-x+x-1\right|=4\\ \)

Dấu "=" xảy ra khi \(1\le x\le5\)

\(\dfrac{12}{\left|y+5\right|+3}\\ \left|y+5\right|\ge0\\ \Rightarrow\left|y+5\right|+3\ge3\\ \Rightarrow\dfrac{12}{\left|y+5\right|+3}\le4\)

Dấu "="xảy ra khi y=-5

Mà \(\left|x-5\right|+\left|x-1\right|=\dfrac{12}{\left|y+5\right|+3}\\ \Rightarrow\left|x-5\right|+\left|x-1\right|=\dfrac{12}{\left|y+5\right|+3}=4\)

Vậy \(\left\{{}\begin{matrix}1\le x\le5\\y=-5\end{matrix}\right.\)

\(\left|2x-5\right|=2-x\\ ĐK:2-x\ge0\\ \Rightarrow x\le2\\ \Rightarrow\left[{}\begin{matrix}2x-5=2-x\\2x-5=x-2\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}3x=7\\x=3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{3}\\x=3\end{matrix}\right.\)

Loại hai TH vì ko tm : x<=2

Vậy x thuộc rỗng

 nam moi hanh phuc

 x + 25 +17 + 2.x = 6 + x  

42+2.x = 6 

2.x = 6- 42

2.x = -36

x = -36 : 2 

x = -18

2,25=225/100=9/4

tỉ sô giữa số lớn và số bé là 9/4

số lớn là

20:(9-4)x9=36

số bé là

36-20=16

Đs lớn 36

      bé 16