a/ a.(b+c)-b(a-c)=ab+ac-ab+bc=ac+bc=c.(a+b) => dpcm

b/ a.(b-c)-a.(b+d)=ab-ac-ab-ad=-ac-ad=-a(c+d) => dpcm

Xet tam giac vuong ADB: AD²+BD²=AB²

=> AB²=2²+12=16

=> AB=4

Xet tam giac vuong ADC : AD²+DC²=AC²

=>AC²=12+6²=48

=> AC\(=\sqrt{48}\)

Ta co : BC=BD+CD=2+6=8 => BC²=64(1)

AB²+AC²=4²+48=16+48=64(2)

Tu (1)(2) : AB²+AC²=BC² => tam giac ABC vuong tai A

a/ /1-2x/=125+75=200

=> 1-2x=200 hoac 1-2x=-200

=> x=-199/2 hoac x=201/2

b/ /x+4/=5-8+2004=2001

=> x+4=2001 hoac x+4=-2001

=> x=1992 hoac x=-2005

c/ /x-9/-1=(-45)-81+2006=1880

=> /x-9/ = 1880+1=1881

=> x-9=1881 hoac x-9=-1881

=> x=1990 hoac x=-1872

2xy+x-14y=21

=> x.(2y+1)-7.(2y+1)+7=21

=>(x-7)(2y+1)=14

=> x-7 va 2y+1∈U(14)=(1,14,2,7,-1,-14,-2,-7)

Ban tu giai ra x,y nha

a/\(\dfrac{8}{x-8}+1+\dfrac{11}{x-11}+1=\dfrac{9}{x-9}+1+\dfrac{10}{x-10}+1\)

=>\(\dfrac{8+x-8}{x-8}+\dfrac{11+x-11}{x-11}=\dfrac{9+x-9}{x-9}+\dfrac{10+x-10}{x-10}\)

=>\(\dfrac{x}{x-8}+\dfrac{x}{x-11}-\dfrac{x}{x-9}-\dfrac{x}{x-10}=0\)

=>x.\(\left(\dfrac{1}{x-8}+\dfrac{1}{x-11}+\dfrac{1}{x-9}+\dfrac{1}{x-10}\right)=0\)

=>x=0

b/\(\dfrac{x}{x-3}-1+\dfrac{x}{x-5}-1=\dfrac{x}{x-4}-1+\dfrac{x}{x-6}-1\)

=>\(\dfrac{x-x+3}{x-3}+\dfrac{x-x+5}{x-5}-\dfrac{x-x+4}{x-4}-\dfrac{x-6+6}{x-6}=0\)

=>\(\dfrac{3}{x-3}+\dfrac{5}{x-5}-\dfrac{4}{x-4}-\dfrac{6}{x-6}=0\)

Đến đây thì bạn giải giống câu a

34.(-84)+17.(-32)=17.2.(-84)+17.(-32)

=17.(-84.2)+17.(-32)

=17.(-168)+17.(-32)

=17.[(-168)+(-32)]=17.(-200)=-3400

Xet tam giac ABC co : A+B+C=180

=> A+C=180-B=180-80=100(1)

Ta co: 3A=2C=> A=2C/3(2)

Tu (1)(2)=> 2C/3+C=100

=> 5C/3=100

=> C=100:5/3=60

=> A=100-C=100=60=40

Vi /x+1/≥0 va /2y-4/≥0

=> /x+1/+/2y-4/≥0

Dau "=" xay ra khi : x+1=0 va 2y-4=0

=> x=-1 va y=2

a/ -3x=-60+30

=> -3x=-30

=> x=(-30):(-3)

=> x=10

Ban oi phai x,y∈Z thi moi lam dc

b/x.y=7

Vi x,y∈U(7)=(1,-1,7,-7)

Với x=1 => y=7 y=1=>x=7

x=-1 =>x=-7 y=-1=>x=-7

x=7 => x=1 y=7=>x=7

x=-7 => x=-1 y=-7=>x=-1

c/(x-1)(y+2)=-7

x-1 va y+2∈U(-7)=(1,-1,7,-7)

Bạn giải giống câu b/ nhưng x,y trái đâu nhé

d/2x-3=5x-7

=>(-3)+7=5x-2x

=>4=3x

=>x=4/3

e/(-2)²-8x=20

=>4-8x=20

=>4-20=8x

=>-16=8x

=>x=-2

f/17-(-31)+3x=2x-(-50)

=>17+31+3x=2x+50

=>49+3x=2x+50

=> 3x-2x=50-49

=> x=1

g/2y²-16=34

=>2y²=34+16

=>2y²=50

=>y²=50:2

=>y²=25=5²=(-5)²

=>y=5 va y=-5

Vi hai so am nhan voi nhau vi mat dau am nen (-2)(-4)=2.4=8