Cho \(a_1\le a_2\le a_3\) và \(b_1\le b_2\le b_3\) ,cmr:
a)\(\dfrac{a_1+a_2}{2}.\dfrac{b_1+b_2}{2}\le\dfrac{a_1b_1+a_2b_2}{2}\)
b)\(\dfrac{a_1+a_2+a_3}{3}.\dfrac{b_1+b_2+b_3}{3}\le\dfrac{a_1b_1+a_2b_2+a_3b_3}{3}\)
áp dụng:\(\left(x+y\right)\left(x^3+y^3\right)\left(x^7+y^7\right)\le4\left(x^{11}+y^{11}\right)\)
\(\forall...
Đọc tiếp
Cho \(a_1\le a_2\le a_3\) và \(b_1\le b_2\le b_3\) ,cmr:
a)\(\dfrac{a_1+a_2}{2}.\dfrac{b_1+b_2}{2}\le\dfrac{a_1b_1+a_2b_2}{2}\)
b)\(\dfrac{a_1+a_2+a_3}{3}.\dfrac{b_1+b_2+b_3}{3}\le\dfrac{a_1b_1+a_2b_2+a_3b_3}{3}\)
áp dụng:\(\left(x+y\right)\left(x^3+y^3\right)\left(x^7+y^7\right)\le4\left(x^{11}+y^{11}\right)\)
\(\forall x,y>0\)
