Question

(-radical din 2+5)la patrat+2(-radical din 2 - 4) ( -radical din 2+5)+(-radical din2 -4)la patrat
Decat 2 este sub radical

Answer 1

(-√2 + 5)^2 +2(-√2 - 4)(-√2 + 5) +(-√2 - 4)^2
....................................................................


[tex]\it(-\sqrt2+5)^2+2(-\sqrt2-4)(-\sqrt2+5)+(-\sqrt2-4)^2 = [/tex]

$=(\it5- \sqrt{\it 2}\it )^2 - \it2(\sqrt2+4)(5-\sqrt2) + (\sqrt2+4)^2=$

$=(\it5-\sqrt2-\sqrt2-4)^2=(1-2\sqrt2)^2=$

$=\it1-4\sqrt2+8=9-4\sqrt2$

Answer 2

$(-\sqrt{2}+5)^2+2(-\sqrt{2}-4)(-\sqrt{2}+5)+ (-\sqrt{2}-4)^2= \\\\\\ = [(-\sqrt{2}+5)+(-\sqrt{2}-4)]^2= \\\\= ( -2\sqrt{2}+1)^2= \\\\ = 8-4\sqrt{2}+1= \\\\ \underline{=9-4\sqrt{2}}$