[tex]3) x+ \frac{1}{x} = 3~(o~ridicam~la~patrat~) \\ \\ (x+ \frac{1}{x})^{2}=3^{2} \\ \\ x^{2} + \frac{1}{ x^{2} } +2*x* \frac{1}{x}=9 \\ \\ x^{2} + \frac{1}{ x^{2} } +2=9 \\ \\ x^{2} + \frac{1}{ x^{2} }=7~(o~ridicam~la~patrat) \\ \\ ( x^{2} + \frac{1}{ x^{2} }) ^{2}=7^{2} \\ \\ x^{4}+ \frac{1}{ x^{4} } +2* x^{2} * \frac{1}{ x^{2} }=49 \\ \\ x^{4}+ \frac{1}{ x^{4} }+2=49 \\ \\ x^{4}+ \frac{1}{ x^{4} }=47 [/tex]
[tex]2) (a;b;c)~d.p.~(0,2; 0,5; 3) \\ \\ \frac{a}{0,2}= \frac{b}{0,5}= \frac{c}{3}=k \\ \\ a=0,2k~~~b=0,5k~~~c=3k \\ \\ 5a+2b+2c=64 \\ 5*0,2k+2*0,5k+2*3k=64 \\ k+k+6k=84 \\ 8k=64 \\ k=8 \\ \\ a=0,2*8=1,6~~~~b=0,5*8=4~~~~c=3*8=24[/tex]
