Cho $x,y$ là 2 số thực bất kì khác 0. Chứng minh rằng: $\frac{4x^2y^2}{(x^2+y^2)^2}+\frac{x^2}{y^2}+\frac{y^2}{x^2}\geq 3$
Cho $x,y$ là 2 số thực bất kì khác 0. Chứng minh rằng: $\frac{4x^2y^2}{(x^2+y^2)^2}+\frac{x^2}{y^2}+\frac{y^2}{x^2}\geq 3$
By Allison
Đáp án:
Giải thích các bước giải:
Đặt biểu thức vế trái là $A$ thì
$$A=\frac{4}{\left ( \frac{x}{y}+\frac{y}{x} \right )^2}+\left ( \frac{x}{y} \right )^2+\left ( \frac{y}{x} \right )^2$$
Đặt $a=\frac{x}{y}~;b=\frac{y}{x}$ thì $ab=1\Rightarrow a^2+b^2\geq 2$
Ta có :
$$A=\frac{4}{(a+b)^2}+a^2+b^2=\frac{4}{a^2+b^2+2}+\frac{a^2+b^2+2}{4}+\frac{3(a^2+b^2+2)}{4}-2\geq 2+3-2=3$$
Đáp án:
Giải thích các bước giảTet is a national and family festival. It is an occasion for every Vietnamese to have a good time while thinking about the last year and the next year. At Tet, spring fairs are organized, streets and public buildings are brightly decorated and almost all shops are crowded with people shopping for Tet. At home, every is tidied, special food is cooked,offerings of food, fresh water, flowers and betel are made on the family altar with burning joss- sticks scenting the air. First-footing is made when the lucky visitor comes and children are given lucky money wrapped in a red tiny envelope. Tet is also a time for peace and love. During Tet, children often behave well and friends, relatives and neighbors give each other best wishes for the new year.