Cho a,b,c,d,e \(\in\)\(R\) . Chứng minh các BĐT sau:
a/ a2 + b2 + c2 \(\ge\) ab + bc + ca
b/ a2 + b2 +1 \(\ge\) ab + a + b
c/ a2 + b2 +c2 + 3 \(\ge\) 2( a + b + c)
d/ a2 + b2 + c2 \(\ge\) 2( ab + bc - ca)
e/ a4 + b4 + c2 +1 \(\ge\) 2a( ab2 - a +c +1)
f/ \(\dfrac{a^2}{4}\)+ b2 + c2 \(\ge\) ab - ac +2bc
g/ a2 (1+b2) + b2 (1+c2) +c2 (1+a2) \(\ge\) 6abc
h/ a2 +b2+ c2+ d2+ e2 \(\ge\) a(b+c+d+e)
i/ \(\dfrac{1}{a}\)+ \(\dfrac{1}{b}\)+\(\dfrac{1}{c}\) \(\ge\)...
Đọc tiếp
Cho a,b,c,d,e \(\in\)\(R\) . Chứng minh các BĐT sau:
a/ a2 + b2 + c2 \(\ge\) ab + bc + ca
b/ a2 + b2 +1 \(\ge\) ab + a + b
c/ a2 + b2 +c2 + 3 \(\ge\) 2( a + b + c)
d/ a2 + b2 + c2 \(\ge\) 2( ab + bc - ca)
e/ a4 + b4 + c2 +1 \(\ge\) 2a( ab2 - a +c +1)
f/ \(\dfrac{a^2}{4}\)+ b2 + c2 \(\ge\) ab - ac +2bc
g/ a2 (1+b2) + b2 (1+c2) +c2 (1+a2) \(\ge\) 6abc
h/ a2 +b2+ c2+ d2+ e2 \(\ge\) a(b+c+d+e)
i/ \(\dfrac{1}{a}\)+ \(\dfrac{1}{b}\)+\(\dfrac{1}{c}\) \(\ge\) \(\dfrac{1}{\sqrt{ab}}\)+\(\dfrac{1}{\sqrt{bc}}\)+\(\dfrac{1}{\sqrt{ca}}\) , (a,b,c > 0)
j/ a+b+c \(\ge\) \(\sqrt{ab}\)+\(\sqrt{bc}\)+\(\sqrt{ca}\) ( a,b,c \(\ge\)0)
