Question

1. (√√2 + 1 - √√2 - 1)² + (√3 + √5 + √3 - √5)²
Primul radical este peste tot iar al doilea doar peste cifra ce urmeaza dupa el!! Hellp!!

Answer 1

$\left(\sqrt{\sqrt2+1}-\sqrt{\sqrt2-1}\right)^2+\left(\sqrt{3+\sqrt5}+\sqrt{3-\sqrt5}\right)^2=$

$=\sqrt2+1-2\sqrt{(\sqrt2-1)(\sqrt2+1)}+\sqrt2-1+3+\sqrt5+$

$+\sqrt{(3-\sqrt5)(3+\sqrt5)}+3-\sqrt5=2\sqrt2-2+6+2=2\sqrt2+6$

Am folosit formulele:

$(a\pm b)^2=a^2\pm 2ab+b^2;\ \ (a-b)(a+b)=a^2-b^2;\ (\sqrt x)^2=x$