\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\Leftrightarrow\frac{ab+bc+ca}{abc}=0\Leftrightarrow ab+bc+ca=0\)
\(\left(a+b+c\right)^2=1\Leftrightarrow a^2+b^2+c^2+2.\left(ab+bc+ca\right)=1\)
\(\Leftrightarrow a^2+b^2+c^2+2.0=1\)
\(\Leftrightarrow a^2+b^2+c^2=1\)
cho a+b+c=0 va a binh phuong+ b binh phuong+ c binh phuing=1 .tinh m=a mu 4 + b mu 4 + c mu 4
B1. Cho f(1)=1008,f(1)+f(2)+...+f(n)=n^2.f(n) f(n)la ham so duong
tinh f(2015)
B2 Cho cac so nguyen to q,p,r,s sao cho cac so sau deu la so nguyen to p^s+s^q,q^s+s^r,r^s+s^p
tim cac so p,q,r,s
B3 co a,b,c duong a mu 3+bmu3=c^3
so sanh a^2015+b^2015 va c^2015
cho a,b,c la 3 so khac 0 va a+b+c=0 chung minh rang 1/a^2+b^2-c^2+1/b^2+c^2-a^2+1/c^2+a^2-b^2=0
cho 1/a + 1/b + 1/c = 1/(a+b+c)
c/m : 1/(a^2015) + 1/(b^2015) + 1/(c^2015) = 1/(a^2015 + 1/b^2015 +1/c^2015).
^ la so mu nha....
cho a+b+c=0 va aa+bb+cc=14 . tinh a mu 4+b mu 4 +c mu 4
1.tìm các nghiem nguyen cua phuong trinh: 54x^3+1=y^3
2.cho x+y=1 và xy khac 0.chung mih \(\frac{x}{y^3-1}+\frac{y}{x^3-1}+\frac{2\left(x-y\right)}{x^2y^2+3}=0\)
3.cho a,b,c la cac so thuc duong.chung minh :\(\left(\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\right)^2+\frac{14abc}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\ge4\)
a) a/b + b/a >_ 2
b) (a+b)(1/a +1/b)>_ 4
c) (a+b+c) (1/a +1/b +1/c)>_9
2. chung minh rang moi a, b la cac so tuy y, ta co :
a) (a-1)(a-3)(a-4)(a-6) +9 >_ 0
b) 4a(a-b)(a+1)(a+b+1) + b2 >_ 0
3. giai phuong trinh | x2 - x + 2| - 3x + 7 = 0
Bai 1:cho a,b,c la do dai 3 canh tam giac
CMR a^2016/b+c-a + b^2016/c+a-b + c^2016/a+b-c >= a^2015 +b^2015+c^2015
Bai 2;cho a,b,c la cac so thuc thoa man:0<=a,b,c<=4 va a+b+c=6
tim GTLN P=a^2+b^2+c^2 +ab+bc+ca
Giup minh voi cac ban !!!
Cho a + b + c = 0 va a^2 + b^2 + c^2 = 1 . khi do , gia tri bieu thuc a^4 + b^4 + c^4 = ????
