\(C=3x^2+x+100\)
=> \(C=3\left(x^2+\frac{1}{3}x\right)+100\)
=> \(C=3\left(x^2+2.x.\frac{1}{6}+\frac{1}{36}\right)+100-\frac{1}{12}\)
=> \(C=3\left(x+\frac{1}{6}\right)^2+99\frac{11}{12}\)
Có \(3\left(x+\frac{1}{6}\right)^2\ge0\)với mọi x
=> \(3\left(x+\frac{1}{6}\right)^2+99\frac{11}{12}\ge99\frac{11}{12}>0\)với mọi x
=> C > 0 với mọi x
=> C luôn dương với mọi x (Đpcm)
a;b;c la cac so duong tim Min B=a/b + b/c + c/a +b/a + c/b + a/c
cho cac so nguyen duong a,b,c thoa man :(a,b,c)=1;ab=c(a+b).Cm a+b la so chinh phuong
cho a,b,c, la cac so duong thoa man a+b+c=1, c/m :1/a+1/b+1/c>=9
Cho a,b,c nguyen duong sao cho a^2/b, b^2/c, c^2/a la cac so nguyen to. cmr a=b=c
CMR voi a,b,c la cac so duong, ta co (a+b+c)(1/a+1/b+1/c)>=9
chung minh rang voi a,b,c la cac so duong ,ta co (a+b+c)(1/a+1/b+1/c)>=9
cho a,b,c la cac so duong thoa man (1/a+1/b+1/c)>=(a+b+c), chung minh a+b+c>=3abc
cho a,b,c,d la cac so nguyen duong doi 1 khac nhau thoa man a/a+b + b/b+c + c/c+d + d/d+a =2
CMR abcd la 1 so chinh phuong
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
