Question

Arătați ca numărul a=(√2-1/2)² +(√2/2+1)²+(1/2-√5)(1/2+√5) este întreg

Answer 1

$a=2- 2*\sqrt{2}* \frac{1}{2} + \frac{1}{4} + \frac{2}{4} +2* \frac{ \sqrt{2} }{2} *1+1+ \frac{1}{4} -5$

$a=2- \sqrt{2} + \frac{3}{4} +\sqrt{2} +1+ \frac{1}{4} -5$

$a=2 + \frac{3}{4} +1+ \frac{1}{4} -5$

$a=\frac{2*4+3+4*1+1-20}{4}$

$a=\frac{8+3+4+1-20}{4}$

$a= \frac{16-20}{4}$

$a=- \frac{4}{4}$

$a=-1$∈Z