đặt A= \(\left(a-b\right)^2\)+(b-c)^2+(c-a)^2=a^2-2ab+b^2+b^2-2bc+c^2+
-2ca+a^2
=2(a^2+b^2+c^2-ab-bc-ca)
=>A=2A
=>A=0
=>(a-b)^2+(b-c)^2+(c-a)^2=0
=>\(\left[{}\begin{matrix}a-b=0\\b-c=0\\c-a=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}a=b\\b=c\\c=a\end{matrix}\right.\)
=>a=b=c (ĐPCM)
Cho a2+b2 +c2 -ab-ac-bc=0
Chứng minh a=b=c
Cho \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\) với a, b, c ≠ 0 và M =\(\dfrac{b^2c^2}{a}+\dfrac{c^2a^2}{b}+\dfrac{a^bb^2}{c}\)
CMR: M = 3abc
giúp mk khẩn cấp vs ạ
(1) (a+b−c)2=a2+b2+c2+2ab−2bc−2ac(a+b−c)2=a2+b2+c2+2ab−2bc−2ac
(3) a3+b3=(a+b)3−3ab(a+b)a3+b3=(a+b)3−3ab(a+b)
(5) (a+b+c)3=a3+b3+c3+3(a+b)(b+c)(c+a)(a+b+c)3=a3+b3+c3+3(a+b)(b+c)(c+a)
(7) (a−b)3+(b−c)3+(c−a)3=3(a−b)(b−c)(c−a)(a−b)3+(b−c)3+(c−a)3=3(a−b)(b−c)(c−a)
(9) (a+b)(b+c)(c+a)=(a+b+c)(ab+bc+ca)−abc(a+b)(b+c)(c+a)=(a+b+c)(ab+bc+ca)−abc
(11) ab3+bc3+ca3−a3b−b3c−c3a=(a+b+c)[(a−b)3+(b−c)3+(c−a)3]3ab3+bc3+ca3−a3b−b3c−c3a=(a+b+c)[(a−b)3+(b−c)3+(c−a)3]3
(1) (a+b−c)2=a2+b2+c2+2ab−2bc−2ac(a+b−c)2=a2+b2+c2+2ab−2bc−2ac
(3) a3+b3=(a+b)3−3ab(a+b)a3+b3=(a+b)3−3ab(a+b)
(5) (a+b+c)3=a3+b3+c3+3(a+b)(b+c)(c+a)(a+b+c)3=a3+b3+c3+3(a+b)(b+c)(c+a)
(7) (a−b)3+(b−c)3+(c−a)3=3(a−b)(b−c)(c−a)(a−b)3+(b−c)3+(c−a)3=3(a−b)(b−c)(c−a)
(9) (a+b)(b+c)(c+a)=(a+b+c)(ab+bc+ca)−abc(a+b)(b+c)(c+a)=(a+b+c)(ab+bc+ca)−abc
(11) ab3+bc3+ca3−a3b−b3c−c3a=(a+b+c)[(a−b)3+(b−c)3+(c−a)3]3ab3+bc3+ca3−a3b−b3c−c3a=(a+b+c)[(a−b)3+(b−c)3+(c−a)3]3
H·y viÕt c¸c biÓu thøc díi d¹ng tæng cña ba b×nh phong;
(a + b + c)2 + a2 + b2 + c2
mình ko biết tổng ba bình phong là gì
Bài 8: a)Chứng minh rằng ( a + b + c)3- a3 – b3 – c3 = 3( a +b)(b +c)( c+ a)
b)a3 +b3 +c3 – 3abc = ( a + b + c)( a2 +b2 + c2)
CMR a = b = c
a, ( a + b + c)^2 = 3( a^2 + b^2 + c^2)
b, ( a - b)^2 + ( b - c)^2 + (c - a)^2 + 4(ab + bc + ca) = 4( a^2 + b^2 + c^2)
Bài 1
Cho \(a^2+b^2+c^2+3=2\left(a+b+c\right)\)
CMR \(a=b=c=1\)
Bài 2
Cho \(\left(a+b+c\right)^2=3\left(ab+ac+bc\right)\)
Cmr \(a=b=c\)
1.CM các hằng đăng thức
a) (a+b+c)^3-a^3-b^3-c^3=3(a+b)(b+c)(c+a)
b)a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)
2.Cho a+b+c=0. CMR: a^3+b^3+c^3=3abc
Giúp mk tí nha mơn nhìu
