cho a,b,c >=0 va \(^{a^{2019}+b^{2019}+c^{2019}=3}\) tim max cua P= \(a^4+b^4+c^4\)

cho a,b,c thoa man \(a\times\sqrt{1-b^2}+b\times\sqrt{1-c^2}+c\times\sqrt{1-a^2}=\dfrac{3}{2}\)

chung minh \(a^2+b^2+c^2=\dfrac{3}{2}\)

tim mim A=\(\dfrac{xy}{z}+\dfrac{yz}{x}\)+\(\dfrac{xz}{y}\)voi x,y,z >0 va x^2+y^2+z^2=1

cái bóng chứ gì

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 \(\dfrac{a^2+b^2+1}{ab}\)

tim min,max

P=\(\dfrac{x^2-3x+2}{x^2+1}\)

Q=\(\dfrac{x^2-xy+2y^2}{x^2-xy+y^2}\)