1, cho các số dương a,b,c ?
Cmr: \(\frac{b}{a^2}+\frac{c}{b^2}+\frac{a}{c^2}\ge\frac{9}{a+b+c}\)
2,tim nghiem nguyen cua he
x4 + y4 =13 x2 y2
x2 - y2 =1 + 2xy
Tim a ,b,c de phuong trinh sau co vo so nghiem
\(\sqrt{x+a\sqrt{x}+b}=c-\sqrt{x}\)
Tim cac gia tri cua m de tap nghiem cua phuong trinh x4 - 2(m-1)x2 -(m-3)=0 co
a, 4 phan tu
b, 3 phan tu
c, 2 phan tu
d, khong co phan tu nao (vo nghiem)
1.Tim a de \(N=\frac{6}{M}\in Z\)biet \(M=\frac{a+2\sqrt{a}+1}{\sqrt{a}}\)
2.tim nghiem nguyen to cua pt:\(x^2-2y^3=1\)
3.Cho a, b,c la 3 canh cua tam giac.CM:\(a^2\left(b+c\right)+b^2\left(c+a\right)+c^2\left(a+b\right)\subseteq a^3+b^3+c^3\)
4.ve do thi ham so \(y=\sqrt{x^2-4x+4}-\sqrt{x^2+4x+4}\)dung do thi. tim GTLN,GTNN.
tim m de phuong trinh sau co nghiem kep roi tim nghiem kep do
a) x^2 -mx-4=0
b)x^2 -2(m-4)x +m^2 +m +3 = 0
Tim m de
m(m-3)x+m-3=0
a,co nghiem duy nhaat
b,vo nghiem
c,co vo so nghiem
Cho P(x)=6x^5+ax^4+bx^3+x^2+cx+450
P(x) chia het cho (x-2),(x-3),(x-5)
tim a,b,c va cac nghiem cua P(x)
1> cho PT : \(x^2-4x+m=0\)
a) Tim m de PT co 2 nghiem phan biet
b) Tim m de phuong trinh co 2 nghiem x1 , x2 thoa man :
\(x1^3+x2^3-5\left(x1^2+x2^2\right)=26\)
a,giai pt (x-3/x-2)^3-(x-3)^3=16
b,tim nghiem nguyen cua pt: 8x^2+23y^2+16x-44y-1180=0