Chung minh phuong trinh sau vo nghiem:
x^6+x^5+x^4+x^3+x^2+x+1=0
giai va bien luan phuong trinh theo tham so m,n
a) (m2+m-2)x+3m2+m-4=0
b) m(mx+2n2)-m3=n2(x+m)
cac ban giup minh voi, mai minh phai nop r
Cho phuong trinh x3 +kx2 -4x -4=0
a) Xac dinh k de phuong trinh co 1 nghiem x=1
b) Voi gia tri k vua tim duoc, tim cac nghiem cua phuong trinh
Puong trinh chua an o mau:
Cho puong trinh 4x2 -25 +k2 +4kx=0 (an x)
a) Giai phuong trinh voi k=0
b) Giai phuong trinh voi k=-3
c) Tim cac gia tri cua k de phuong trinh nhan x=-2 lam nghiem
bai 1: cho phuong trinh: x2+(a+b).x-2.(a2-ab+b2) =0. CMR: luon co nghiem voi moi ab
cac ban oi giup minh sap di hoc roi.
chung minh rang phuong trinh sau co 3 nghiem phan biet
\(\frac{x-a}{b}+\frac{x-b}{a}=\frac{b}{x-a}+\frac{a}{x-b}\)
voi \(a,b\ne0;a\ne b;a\ne-b\)
cho a va b la hai so tu nhien. biet a chia cho 5 du 1 ; b chia cho 5 du 4. chung minh (b-a)(b+a) chia cho 4
chung minh 2n^2(n+1)-2n(n^2+n-3) chia het cho 6 voi moi so nguyen n
chung minh n( 3-2n)-(n-1)(1+4n)-1 chia het cho 6 voi moi so nguyen n
bai 1: cho phuong trinh: x2+(a+b).x-2.(a2-ab+b2) =0. CMR: luon co nghiem voi moi ab
cac ban oi giup minh bai nay kho mong cac ban thu suc
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 :\(\left(\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\right)^2+\frac{14abc}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\ge4\)
