1.
x^2-4x+4=-2x^2+8x-6
x^2+2x^2-4x-8x+4+6=0
3x^2-12x+10=0
delta=144-120=24 =>√delata=2√6
x1=(12-2√6)/6
x2=(12+2√6)/6
2.
i)
\frac{1}{a^2 +bc} \leq \frac{1}{4} ( \frac{1}{ab} + \frac{1}{ac})\\
\frac{1}{a^2 +bc} \leq \frac{1}{4} ( \frac{ac+ab}{ab})\\ \\
4ab \leq (a^2 +bc)(ac+ab)\\
4ab \leq a^3c+a^3b+abc^2+ab^2c \\
4ab \leq a^3(c+b)+abc(c+b)\\
4ab \leq (a^3+abc)(c+b)\\
=> oricare ar fi a, b, c, 4ab \leq (a^3+abc)(c+b)
ii) [tex] \frac{1}{a^2+bc}+ \frac{1}{b^2+ac} + \frac{1}{c^2+ab} \leq \frac{1}{2} ( \frac{1}{ab}+ \frac{1}{bc} + \frac{1}{ca} )\\
\\
\frac{b^2+ac+c^2+ab+a^2+bc+c^2+ab+a^2+bc+b^2+ac}{(a^2+bc)(b^2+ac)(c^2+ab)} \leq \frac{1}{2} \frac{bc+ac+ab+ac+ab+bc}{a^2b^2c^2} \\
[/tex]
