chung to rang:
a,(a+b)-(b-a)+c=2a+c
b,-2b=-(a+b-c)+(a-b-c)
cho ti le thuc a/b = c/d ,chung to rang a,3a + 2b / a = 3c + 2d / c ; b, 2a - 3b/ b = 2c - 3d / b ; c, a/ a-2b = c/c-2d giup minh voi dang can gap
Đặt a/b=c/d=k
=>a=bk; c=dk
a: \(\dfrac{3a+2b}{a}=\dfrac{3bk+2b}{bk}=\dfrac{3k+2}{k}\)
\(\dfrac{3c+2d}{c}=\dfrac{3dk+2d}{dk}=\dfrac{3k+2}{k}\)
Do đó: \(\dfrac{3a+2b}{a}=\dfrac{3c+2d}{c}\)
b: \(\dfrac{2a-3b}{b}=\dfrac{2bk-3b}{b}=2k-3\)
\(\dfrac{2c-3d}{d}=\dfrac{2dk-3d}{d}=2k-3\)
Do đó: \(\dfrac{2a-3b}{b}=\dfrac{2c-3d}{d}\)
c: \(\dfrac{a}{a-2b}=\dfrac{bk}{bk-2b}=\dfrac{k}{k-2}\)
\(\dfrac{c}{c-2d}=\dfrac{dk}{dk-2d}=\dfrac{k}{k-2}\)
Do đó: \(\dfrac{a}{a-2b}=\dfrac{c}{c-2d}\)
chung to rang
a,(a+b)-(b-a)+c=2a+c
b,-2b=-(a+b-c)+(a-b-c)
ai lam dc cho like
a.(a+b)-(b+a)+c=
=a+b-b+a+c
=2a+c (đpcm)
Vậy (a+b)-(b-a)+c=2a+c
b.-(a+b-c)+(a-b-c)=
=-a-b+c+a-b-c
=-b-b
=-2b (đpcm)
Vậy -2b=-(a+b+c)+(a-b-c)
NHớ tick cho mình nha!!!!!!!!!
cho a/b-2c=b/c-2a=c/a-2b tinh A=a/b+2c+b/c+2a+c/a+2b
giup to voi
BAI 2 CHUNG TO
1, (a -b +c) - (a+c ) =-b
2, (a + b ) -( b-a0 + c =2a+c
3, -(a+b -c) + (a-b-c )=-2b
4,a nhan ( b+ c) -a nhan (b+d) =a (c-d)
5,a nhan (b -c) =a (d +c )= a nhan ( b +d)
\(\left(a-b+c\right)-\left(a+c\right)\)
\(=a-b+c-a-c\)
\(=\left(a-a\right)+\left(c-c\right)-b\)
\(=0+0-b\)
\(=0-b\)
\(=-b\)
1) (a - b + c) - (a + c)
= a - b + c - a - c
= (a - a) - b + (c - c)
= 0 - b + 0 = -b
2) (a + b) - (b - a) + c
= a + b - b + a + c
= (a + a) + (b - b) + c
= 2a + 0 + c = 2a + c
3) -(a + b - c) + (a - b - c)
= -a - b + c + a - b - c
= (-a + a) - (b + b) + (c - c)
= 0 - 2b + 0 = -2b
4) a(b + c) - a(b + d)
= ab + ac - ab - ad
= (ab - ab) + a(c - d)
= 0 + a(c - d) = a(c - d)
5) tự lm
\(\left(a+b\right)-\left(b-a\right)+c\)
\(=a+b-b+a+c\)
\(=\left(a+a\right)+\left(b-b\right)+c\)
\(=2a+0+c\)
\(=2a+c\)
cho a+b+c=0.chung minh rang:a^3+b^3+c^3=3abc
Do \(a+b+c=0\Rightarrow a+b=-c\)
Ta có hằng đẳng thức: \(\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3\)
nên \(a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)\)
Do đó: \(a^3+b^3+c^3=\left(a+b\right)^3+c^3-3ab\left(a+b\right)=\left(-c\right)^3+c^3-3ab.\left(-c\right)=3abc\left(đpcm\right)\)
cho a,b,c la cac so thuc duong. chung minh rang 2a/(b+c)+2b/(c+a)+2c/(a+b)>=((a-b)^2+(b-c)^2+(c-a)^2)/(a+b+c)^2
cho a/c=c/b chung minh rang:a2+c2/b2+c2=a/b
theo đề bài ta có:\(\frac{a}{c}=\frac{c}{b}\Rightarrow c^2=ab\)
ta có:
\(\frac{a^2+c^2}{b^2+c^2}=\frac{a^2+ab}{b^2+ab}=\frac{a\left(a+b\right)}{b\left(a+b\right)}=\frac{a}{b}\left(đpcm\right)\)
cho 2a+b/a-2b = 2c+d/c-2d chung minh a/b = c/d
Áp dụng tính chất dãy tỉ số bằng nhau
\(\frac{x}{5}=\frac{y}{7}=\frac{z}{9}=\frac{x-y+z}{5-7+9}=\frac{315}{7}=45\)
suy ra: x/5 = 45 => x = 225
y/7 = 45 => y = 315
z/9 = 45 => z = 405
Cho 0<=a,b,c<=1. Chung minh 2(a^3+b^3+c^3)<=3+a^2b+b^2c+c^2a