Tích hai đường chéo là:

`15xx2=30(cm^2)`

Độ dài đường chéo BD là:

`30:5=6(cm)`

Nửa chu vi là :

`240:2=120(m)`

Chiều dài thửa ruộng là:

`(120+20):2=70(m)`

Chiều rộng thửa ruộng là:

`70-20=50(m)`

Diện tích thửa ruộng là:

`70xx50=3500(m^2)`

`x-y+sqrt(xy^2)-sqrt(y^3)`

`=(sqrtx-sqrty)(sqrtx+sqrty)+sqrt(y^2)(sqrtx-sqrty)`

`=(sqrtx-sqrty)(sqrtx+sqrty+y)`

`150-2/3`

`=(150xx3-2)/3`

`=(450-2)/3`

`=448/3`

`50,8xx49,2`

`=(50+0,8)xx(50-0,8)`

`=50^2-(0,8)^2`

`=2500-0,64`

`=2499,36`

`9.27^n=3^5`

`=>3^2 .(3^3)^n=3^5`

`=>3^(3n)=3^5:3^2=3^3`

`=>3n=3`

`=>n=1`

`1)2A=2+2^2+2^3+...+2^2006`

`2)2A-A=2+2^2+2^3+...+2^2006-1-...-2^2005`

`=>A=(2-2)+...+2^2006-1`

`=2^2006-1(đpcm)`

`1)2A=2+2^2+2^3+2^4+2^5+2^6`

`2)2A-A=2+2^2+2^3+2^4+2^5+2^6-1-....-2^5`

`=2^6-1`

Ta có:

`1/5m=1/5xx100=20cm`

mà `20cm<30cm`

`=>1/5m<30cm`

`1)A = 1+2¹+2²+...+2²⁰⁰⁵`

`=>2A =2¹+2²+...+2^2006`

`2)2A-A=2+2^2+...+2^2006-1-2-...-2^2005`

`=>A=2^2006-1`

`1)2A=2(1+2^1+2^2+2^3+2^4+2^5)`

`=2+2^2+2^3+2^4+2^6+2^5`

`2)2A-A=2+2^2+2^3+2^4+2^5+2^6-1-2-2^2-2^3-2^4-2^5`

`=2^6-1`

`sqrt(x^2)<3`

`<=>$\left|x\right|$<3`

`<=>[(x> -3),(x<3):}`

`<=>-3<x<3`

Ta có:

`5sqrt3=sqrt(25.3)=sqrt75`

`8=sqrt64`

Vì `sqrt75>sqrt64`

`=>5sqrt3>8`

`Q=9/2P`

`=18/(2(sqrtx+2))`

`=9/(sqrtx+2)`

`Q in ZZ<=>9/(sqrtx+2)inZZ`

`=>9vdots sqrtx+2`

`=>sqrtx+2inU(9)={+-1;+-3;+-9}`

`=>[(sqrtx+2=3),(sqrtx+2=9):}`

`<=>[(sqrtx=1),(sqrtx=7):}`

`<=>[(x=1),(x=49):}(n)`

`a)(x^3-x^2+x+3):(x+1)`

`=(x^3+x^2-2x^2-2x+3x+3):(x+1)`

`=[x^2(x+1)-2x(x+1)+3(x+1)]:(x+1)`

`=(x+1)(x^2-2x+3):(x+1)`

`=x^2-2x+3`

`b)(x^3-6x^2-9x+14):(x-7)`

`=(x^3-7x^2+x^2-7x-2x+14):(x-7)`

`=[x^2(x-7)+x(x-7)-2(x-7)]:(x-7)`

`=(x-7)(x^2+x-2):(x-7)`

`=x^2+x-2`

`99xx58`

`=5742`

`-9/13xx(-4/5)`

`=9/13xx4/5`

`=36/85`

`-0,7:3/2`

`=-7/10xx2/3`

`=-7/5xx1/3`

`=-7/15`

`-7/6: 1 5/7`

`=-7/6 : 12/7`

`=-7/6xx7/12`

`=-49/72`

`(-7)-(-5/8)`

`=-7+5/8`

`=-51/8`

`(16^2-63^2):8^3`

`=16^2:8^3-63^2:8^3`

`=1/2-63^2/8^3`

`(a+b+c)^3-a^3-b^3-c^3`

`=(a+b)^3+3(a+b)^2c+3(a+b)c+c^3-a^3-b^3-c^3`

`=a^3+3a^2b+3ab^2+b^3+3c(a+b)^2+3c^2(a+b)-a^3-b^3`

`=3(a+b)(ac +bc+c^2)+3ab(a+b)`

`=3(a+b)(ac+bc+c^2+ab)`

`=3(a+b)[c(a+c)+b(a+c)]`

`=3(a+b)(a+c)(b+c)(đpcm)`

`(-3x)^4yz^5:27x^2yz^2`

`=81x^4yz^5:27x^2yz^2`

`=3x^2z^3`