1) Cho ax^2+bx+c0 co nghiem x_1vax_2; cy^2+dy+a0 co nghiem y_1vay_2
CM: x_1^2+x_2^2+y_1^2+y_2^24
2) Cho a,b,cin Zleft(ane0right);m,nin Qleft(nne0right);pin N ko chinh phuong
Biet ax^2+bx+c0 co nghiem x_1m+nsqrt{p}
CM: x_2m-nsqrt{p} la nghiem con lai
3) Cho a,bin N* t/m a^2+b^2+1⋮ab
Tinh dfrac{a^2+b^2+1}{ab}
Đọc tiếp
1) Cho \(ax^2+bx+c=0\) co nghiem \(x_1va\)\(x_2\); \(cy^2+dy+a=0\) co nghiem \(y_1va\)\(y_2\)
CM: \(x_1^2+x_2^2+y_1^2+y_2^2>=4\)
2) Cho \(a,b,c\in Z\left(a\ne0\right);m,n\in Q\left(n\ne0\right);p\in N\) ko chinh phuong
Biet \(ax^2+bx+c=0\) co nghiem \(x_1=m+n\sqrt{p}\)
CM: \(x_2=m-n\sqrt{p}\) la nghiem con lai
3) Cho \(a,b\in N\)* t/m \(a^2+b^2+1⋮ab\)
Tinh \(\dfrac{a^2+b^2+1}{ab}\)
