Let y=2+2,z=2−2 and x=y+z, then x is - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

Given $y = \sqrt{2 + \sqrt{2}}, z = \sqrt{2 - \sqrt{2}}$

$∴ x = y + z = \sqrt{2 + \sqrt{2}} + \sqrt{2 - \sqrt{2}}$

$x^{2} = (2 + \sqrt{2}) + (2 - \sqrt{2}) + 2 \sqrt{(2 + \sqrt{2}) (2 - \sqrt{2})}$

$x^{2} = 4 + 2 \sqrt{2}$

$x^{2} = 2 (2 + \sqrt{2})$

$x = \sqrt{2} . \sqrt{2 + \sqrt{2}}$

Let $y = \sqrt{2 + \sqrt{2}}, z = \sqrt{2 - \sqrt{2}}$ and $x = y + z$ , then $x$ is