cho bieu thuc

P\(\left(x\right)=\dfrac{20x^2+120x+180}{\left(3x+5\right)^2-4x^2}+\dfrac{5x^2-125}{9x^2-\left(2x+5\right)^2}-\dfrac{\left(2x+3\right)^2-x^2}{3\left(x^2+8x+15\right)}\)

Tim gia tri nguyen cua x de P(x) co gia tri nguyen

2kg

tích nha

cho a>1,b>1.Chung minh rang :

\(\dfrac{a^2}{b-1}+\dfrac{b^2}{a-1}\ge8\)

cho so thuc a>3 . Tim gia tri nho nhat cua bieu thuc :

f(a)=\(a+\dfrac{25}{a-3}\)

cho 3 so thuc x,y,z khac khong va thoa man hai dieu kien \(ax^3=by^3=cz^3\) va \(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=1\)

chung minh rang : \(\sqrt[3]{ax^2+by^2+cz^2}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}\)

Cho 3 so duong a,b,c thoa man dieu kien : a+b+c=1. Chung minh rang

\(\sqrt{4a+1}+\sqrt{4b+1}+\sqrt{4c+1}< 5\)

Tim gia tri nho nhat cua bieu thuc :

f(x,y)=\(\dfrac{3x^2+2y^2}{2005xy}\) voi xy \(\ne\) 0

cho 3 so a,b,c thoa man dieu kien : \(\left\{{}\begin{matrix}a+b+c=1\\\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\end{matrix}\right.\)

tinh gia tri cua bieu thuc T=\(a^2+b^2+c^2\)

giai phuong trinh : 2x-1=x\(\sqrt{x}\)

Cho phuong trinh : x+m=\(\sqrt{x+1}\) (1)

1/giai phuong trinh (1) khi m=1

2/giai va bien luan phuong trinh (1)theo m