Question

Aratati ca : a=(1/2 -radical din3)^2+(radical di3/2+1)^2+(1-radical din5)(1+ radical din5) este nr intreg

Answer 1

$a=(\frac{1}{2}-\sqrt{3})^{2}+(\frac{\sqrt{3}}{2}+1)^{2}+(1-\sqrt{5})(1+\sqrt{5})=$

$(\frac{1}{4}-2\cdot\frac{1}{2}\cdot\sqrt{3}+3)+(\frac{3}{4}}+2\cdot\frac{\sqrt{3}}{2}+1^{2}})+(1-5)=$

$(\frac{1}{4}+\frac{3}{4})=\frac{4}{4}=1$

Answer 2

Rezolvarea in atasament.