\(a\left(a+b\right)\left(a+c\right)=b\left(b+c\right)\left(b+a\right)\)
\(\Leftrightarrow\left(a+b\right)\left(a^2+ac-b^2-bc\right)=0\)
\(\Leftrightarrow\left(a+b\right)\left[\left(a+b\right)\left(a-b\right)+c\left(a-b\right)\right]=0\)
\(\Leftrightarrow\left(a+b\right)\left(a-b\right)\left(a+b+c\right)=0\)
=>a+b+c=0
Cho a + b + c = 0, abc khác 0. Tính giá trị biểu thức a^2/a^2-b^2-c^2 + b^2/b^2-c^2-a^2 + c^2/c^2-a^2-b^2
cho a;b;c khác 0 và 1/a+1/b+1/c=0.Chứng minh rằng 1/a3+1/b3+1/c3=3/abc
Cho \(\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}=1\)
CM:\(\frac{a^2}{b+c}+\frac{b^2}{a+c}+\frac{c^2}{a+b}=0\)
1. Cho a + b + c = 0. CM:
a/ a3 + b3 + c3 = 3abc.
b/ (ab + bc + ca)2 = a2b2 + b2c2 + c2a2.
c/ a4 + b4 + c4 = 2(ab + bc +ca)2.
2. Cho a + b + c + d = 0. CM:
a3 + b3 + c3 + d3 = 3(b + c)(ad - bc)
Cho a,bc thuộc R . Cm
\(\dfrac{ab}{c}+\dfrac{bc}{a}+\dfrac{ca}{b}\ge a+b+c\left(vớia,b,c>0\right)\)
choa+b+c=0.cm a^4+b^4+c^4=[(a^2+b^2+c^2)]^2/2
Cho a;b;c;d \(\in\) Z .CM : (a-b).(a-c).(a-d).(b-c).(b-d).(c-d) chia hết 12
Cho a,b,c >0 .CMR:
\(\dfrac{a}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{c+a}< \sqrt{\dfrac{b}{c+a}}+\sqrt{\dfrac{a}{c+b}}+\sqrt{\dfrac{c}{a+b}}\)
cho a+b+c=0
cmr M=N=P biết
M=a(a+b)(a+c)
N=b(b+c)(b+a)
P=c(c+a)(c+b)
