Question

1.tìm a,b,c,d,e,f biết: a²+b²+c²+d²+e²+f²+3/7=ab+bc+cd+de+ef+f

2.chứng minh: (a+b+c+d)²>=8/3(ab+ac+ad+bc+bd+cd)

m.n giúp mình vs ^^

Answer 1

2/ Ta có \(\left(a+b+c+d\right)^2\ge\frac{8}{3}\left(ab+ac+ad+bc+bd+cd\right)\)

\(\Leftrightarrow a^2+b^2+c^2+d^2+2\left(ab+ac+ad+bc+bd+cd\right)\ge\frac{8}{3}\left(ab+ac+ad+bc+bd+cd\right)\)

\(\Leftrightarrow3\left(a^2+b^2+c^2+d^2\right)+6\left(ab+ac+ad+bc+bd+cd\right)\ge8\left(ab+ac+ad+bc+bd+cd\right)\)

\(\Leftrightarrow\left(a^2-2ab+b^2\right)+\left(a^2-2ac+c^2\right)+\left(a^2-2ad+d^2\right)+\left(b^2-2bc+c^2\right)+\left(b^2-2bd+d^2\right)+\left(c^2-2cd+d^2\right)\ge0\)

\(\Leftrightarrow\left(a-b\right)^2+\left(a-c\right)^2+\left(a-d\right)^2+\left(b-c\right)^2+\left(b-d\right)^2+\left(c-d\right)^2\ge0\)(luôn đúng)

Vậy bđt ban đầu được chứng minh.

Answer 2

Ui đau đầu quá !

Answer 3

lang nha lang nhang cha hieu gi ca