4. a)
[tex] \sqrt{7-2\sqrt{6}}=\sqrt{6-2\sqrt{6}+1}=\sqrt{(\sqrt{6}-1)^{2}}= \sqrt{6}-1
[/tex]
[tex] \sqrt{10-4\sqrt{6}}=\sqrt{6-4\sqrt{6}+4}=\sqrt{(\sqrt{6}-2)^{2}}= \sqrt{6}-2[/tex]
[tex] \sqrt{7+2\sqrt{6}}=\sqrt{6+2\sqrt{6}+1}=\sqrt{(\sqrt{6}+1)^{2}}= \sqrt{6}+1 [/tex]
Atunci x=√6-1-2(√6-2)+√6+1=√6-1-2√6+4+√6+1=4=2² deci este patrat perfect
b) -x²+12x-28=-(x²-12x+28)=-(x²-12x+36-8)=-[(x-6)²-8]=-(x-6)²+8
Valoarea expresiei este maxima atunci cand x=6.⇒valoarea expresiei cand x=6 este 8
5. (x+1/x)²=9²⇒x²+2x/x+1/x²=81⇒x²+2+1/x²=81⇒x²+1/x²=81-2⇒x²+1/x²=79
