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14:
a: Xét ΔHNM vuông tại H và ΔMNP vuông tại M có
góc N chung
=>ΔHNM đồng dạng với ΔMNP
b: NP=căn 3^2+4^2=5cm
MH=3*4/5=2,4cm
NH=3^2/5=1,8cm
13:
a: 3x+5=x-5
=>2x=-10
=>x=-5
b: (x-2)(2x+5)=0
=>x-2=0 hoặc 2x+5=0
=>x=2 hoặc x=-5/2
c: =>2(5x-2)=3(3x+1)
=>10x-4=9x+3
=>x=7
d: =>(3x+6-x+1)/(x+2)(x-1)=17-3x/(x+2)(x-1)
=>2x+7=17-3x
=>5x=10
=>x=2
a: \(VP=a^3+b^3+c^3-3bac\)
\(=\left(a+b\right)^3+c^3-3ab\left(a+b\right)-3abc\)
\(=\left(a+b+c\right)\left[\left(a+b\right)^2-c\left(a+b\right)+c^2\right]-3ab\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2-3ab\right)\)
\(=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ac\right)=VT\)
b: \(VT=\left(3a+2b-1\right)\left(a+5\right)-2b\left(a-2\right)\)
\(=3a^2+15a+2ab+10b-a-5-2ab+4b\)
\(=3a^2+14a+14b-5\)
\(VP=\left(3a+5\right)\left(a+3\right)+2\left(7b-10\right)\)
\(=3a^2+9a+5a+15+14b-20\)
\(=3a^2+14a+14b-5\)
=>VT=VP
c: \(VT=a\left(b-x\right)+x\left(a+b\right)\)
\(=ab-ax+ax+bx\)
\(=ab+bx=b\left(a+x\right)=VP\)
d: \(VT=a\left(b-c\right)-b\left(a+c\right)+c\left(a-b\right)\)
\(=ab-ac-ab-bc+ca-cb\)
\(=-2bc\)
=VP
1 If we continue polluting the air, the environment will be affected seriously
2 If we don't stop damaging birds' homes, there will be fewer birds left
3 If we continue polluting the water, there will be more disease in people and animals
4 If we keep polluting the land, the soil will not be safe enough for us to grow food in
5 If we use public transportation when we need, there will be less air pollution
12 Daniel signs up for a clean-up campaign so that he can join in it
13 People in my neighborhood clean the park up so that their children will have a nice place to play
14 Almost all the students in my school plant trees so that they can have much fresher air
o: x^4+x^3+x^2-1
=x^3(x+1)+(x-1)(x+1)
=(x+1)(x^3+x-1)
q: \(=\left(x^3-y^3\right)+xy\left(x-y\right)\)
=(x-y)(x^2+xy+y^2)+xy(x-y)
=(x-y)(x^2+2xy+y^2)
=(x-y)(x+y)^2
s: =(2xy)^2-(x^2+y^2-1)^2
=(2xy-x^2-y^2+1)(2xy+x^2+y^2-1)
=[1-(x^2-2xy+y^2]+[(x+y)^2-1]
=(1-x+y)(1+x-y)(x+y-1)(x+y+1)
u: =(x^2-y^2)-4(x+y)
=(x+y)(x-y)-4(x+y)
=(x+y)(x-y-4)
x: =(x^3-y^3)-(3x-3y)
=(x-y)(x^2+xy+y^2)-3(x-y)
=(x-y)(x^2+xy+y^2-3)
z: =3(x-y)+(x^2-2xy+y^2)
=3(x-y)+(x-y)^2
=(x-y)(x-y+3)
o) \(x^4+x^3+x^2-1\)
\(=\left(x^4+x^3\right)+\left(x^2-1\right)\)
\(=x^3\left(x+1\right)+\left(x+1\right)\left(x-1\right)\)
\(=\left(x+1\right)\left(x^3+x-1\right)\)
q) \(x^3+x^2y-xy^2-y^3\)
\(=\left(x^3+x^2y\right)-\left(xy^2+y^3\right)\)
\(=x^2\left(x+y\right)-y^2\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-y^2\right)\)
\(=\left(x+y\right)^2\left(x-y\right)\)
s) \(4x^2y^2-\left(x^2+y^2-1\right)^2\)
\(=\left(2xy\right)^2-\left(x^2+y^2-1\right)^2\)
\(=\left(2xy-x^2-y^2+1\right)\left(2xy+x^2+y^2-1\right)\)
\(=-\left(x^2-2xy+y^2-1\right)\left(x^2+2xy+y^2-1\right)\)
\(=-\left(x-y-1\right)\left(x-y+1\right)\left(x+y+1\right)\left(x+y-1\right)\)
u) \(x^2-y^2-4x-4y\)
\(=\left(x^2-y^2\right)-\left(4x+4y\right)\)
\(=\left(x+y\right)\left(x-y\right)-4\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-4\right)\)
x) \(x^3-y^3-3x+3y\)
\(=\left(x^3-y^3\right)-\left(3x-3y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)-3\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2-3\right)\)
z) \(3x-3y+x^2-2xy+y^2\)
\(=\left(3x-3y\right)+\left(x^2-2xy+y^2\right)\)
\(=3\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x-y\right)\left(3+x-y\right)\)
a) ∆ABC vuông tại A
⇒ BC² = AC² + AB² (Pytago)
= 10² + 5²
= 125
⇒ BC = 55 (cm)
AM là đường trung tuyến ứng với cạnh huyền BC
⇒ AM = BC : 2 = 5√5/2 (cm)
b) ∆ABC vuông tại A
⇒ BC² = AB² + AC² (Pytago)
= 24² + 7²
= 625
⇒ BC = 25 (cm)
AM là đường trung tuyến ứng với cạnh huyền BC
⇒ AM = BC : 2 = 25/2 (cm)
c) ∆ABC vuông tại A
⇒ BC² = AB² + AC² (Pytago)
= 4² + 3²
= 25
⇒ BC = 5 (cm)
AM là đường trung tuyến ứng với cạnh huyền BC
⇒ AM = BC : 2 = 5/2 (cm)
Em cảm ơn nhiều ạ 😍❤️