\(\left(a+b+c\right)^2+\left(a-b-c\right)^2\)
\(=a^2+b^2+c^2+2ab+2bc+2ac+a^2+b^2+c^2-2ab-2ac+2bc\)
\(=2a^2+2b^2+2c^2+4bc\)
\(=2\left(a^2+b^2+c^2+2bc\right)\)
CMR
a) (a2-b2)2+(2ab)2= (a2+b2)2
b) (ax+b)2+(a-bx)2+c2x2+c2=(a2+b2+c2).(x2+1)
c) (a+b+c)3= a3+b3+c3+3.(a+b).(b+c).(c+a)
d) (a+b).(b+c).(c+a)=(a+b+c).(ab+bc+ca)-abc
e) ab.(a+b)-bc.(b+c)+ac.(a-c)=(a+b).(b+c).(a-c)
f) 2bc.(b+2c)+2a.(c-2a)-2ab.(a+2b-7abc)= (b+2c).(c-2a).(a+2b)
Cho a+b+c=0. Tính \(A=\dfrac{a^2}{a^2-b^2-c^2}+\dfrac{b^2}{b^2-c^2-a^2}+\dfrac{c^2}{c^2-a^2-b^2}\)
Chứng minh hằng đẳng thức:
a)(a+b+c)^2+a^2+b^2+c^2=(a+b)^2+(b+c)^2+(c+a)^2
Cho a,b,c khác o thỏa mãn: \(\dfrac{a^2}{a+b}+\dfrac{b^2}{b+c}+\dfrac{c^2}{c+a}=\dfrac{16}{7}\)Tính \(P=\dfrac{a^2}{a+c}+\dfrac{b^2}{b+a}+\dfrac{c^2}{c+b}\)
chứng minh 1/2(a+b+c)[(a-b)^2+(b-c)^2+(c-a)^2]=a^3+b^3+c^3-3abc
Cho \(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}=1.CM\dfrac{a^2}{b+c}+\dfrac{b^2}{c+a}+\dfrac{c^2}{a+b}=0\)
Cho a,b,c khác 0 thỏa :a+b=c+d và a^2+b^2=c^2+d^2 CMR : a^2006+b^2006=c^2006+d^2006
M.n giúp mình nha :))
a.(b-c).(b+c-c)2 + c.(a-b).(a+b-c)2 - b.(a-c).(a+c-b)
Cho a,b,c thỏa mãn a+b+c=abc. Chứncg minh: a.(b2-1).(c2-1)+b.(a2-1).(c2-1)+c.(a2-1).(b2-1)=4a.b.c
a.(b-c).(b+c-c)2 +c.(a-b).(a+b-c)2 - b.(a-c).(a+c-b)
Mình mới lập nick, mọi người giúp mình nha :)))
