chung minh dang thuc (a+b).(c+d)-(a+d).(b+c)
chung minh dang thuc
[a+b].[c+d]-[a+d].[b+c]=[a-c].[d-b]
(a+b)(c+d)-(a+d)(b+c)=ac+bc+ad+bd-ab-ac-cd-bd
=bc+ad-ab-cd=a(d-b)-c(d-b)=(a-c)(d-b)
chung minh dang thuc sau la sai:
a+b+c-d=a-b+c-d
Không ai trả lời được à,câu này dễ mà
chung minh dang thuc
a, [ b+c ]-b. [ a -c]= [ a+ b].c
b, [b-c ]-a. [b+d]=a.[c+d]
chung minh dang thuc
a.( b - c ) - a ( b + d ) = -a ( c + d )
giup minh voi lam onnnnn.......
a.(b-c)-a.(b+d)=-a.(c+d)
a.b-a.c-a.b+a.d=-a.(c+d)
(a.b-a.b)-(a.c+a.d)=-a.(c+d)
0-a.(c+d)=-a.(c+d)
-a.(c+d)=-a.(c+d)
Vậy a.(b-c)-a.(b+d)=-a.(c+d).
voi a,b,c,d la cac so duong thoa man a*b = c*d = 1. Chung minh bat dang thuc ( a+b )*( c+d ) + 4 >= 2( a+b+c+d )
voi a,b,c,d, la cac so duong thoa man a*b = c*d =1 chung minh bat dang thuc : ( a+b )*( c+d ) +4 >= 2*( a+b+c+d ) cac ban oi giup minh voi OK
cho a,b,c,d la cac so thuc thoa ma dang thuc a+b+c+d=0.chung minh rang:
\(a^3+b^3+c^3+d^3=3\left(b+d\right)\left(ac-bd\right)\)
Ta có \(a+b+c+d=0\Leftrightarrow a+c=-\left(b+d\right)\Leftrightarrow\left(a+c\right)^3=\left[-\left(b+d\right)\right]^3\Leftrightarrow a^3+3a^2c+3ac^2+c^3=-b^3-3b^2d-3bd^2-d^3\Leftrightarrow a^3+b^3+c^3+d^3=-3a^2c-3ac^2-3b^2d-3bd^2\Leftrightarrow a^3+b^3+c^3+d^3=-3ac\left(a+c\right)-3bd\left(b+d\right)\Leftrightarrow a^3+b^3+c^3+d^3=3ac\left(b+d\right)-3bd\left(b+d\right)\Leftrightarrow a^3+b^3+c^3+d^3=3\left(b+d\right)\left(ac-bd\right)\)Vậy \(a+b+c+d=0\) thì \(a^3+b^3+c^3+d^3=3\left(b+d\right)\left(ac-bd\right)\)
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: \(\dfrac{a}{a-2b}=\dfrac{c}{c-2d}\)
Cho a, b, c,d la cac so thuc . Chung minh bat dang thuc sau:
a2 + b2 +c2 +d2 +e2 >= ab +ac + ad +ae
Lam giup minh nhe cac ban minh can gap lam
\(a^2+b^2+c^2+d^2+e^2\ge ab+ac+ad+ae\left(1\right)\)
\(\Leftrightarrow a^2+b^2+c^2+d^2+e^2-a\left(b-c-d-e\right)\ge0\)
\(\Leftrightarrow\left(b^2-ab+\frac{1}{4}a^2\right)+\left(c^2-ac+\frac{1}{4}a^2\right)+\left(d^2-ad+\frac{1}{4}a^2\right)+\left(e^2-ae+\frac{1}{4}a^2\right)\ge0\)
\(\Leftrightarrow\left(b+\frac{1}{2}a\right)^2+\left(c+\frac{1}{2}a\right)^2+\left(d+\frac{1}{2}a\right)^2+\left(e+\frac{1}{2}a\right)^2\ge0\left(2\right)\)
( 2 ) đúng => ( 1 ) đúng