Question

aratati ca a=(radical din 5-2radical din 6 - radical din 5+ 2radical6) la patrat este numar natural.
Repedeeee va rooogg

Answer 1

a=[√(5-2√6)-√(5+2√6)]²
√(5-2√6)=√(5-√24)
$\sqrt{5- \sqrt{24} } = \sqrt{ \frac{5+ \sqrt{25-24} }{2} } - \sqrt{ \frac{5- \sqrt{25-24} }{2} }$
√(5-√24)=√3-√2
√(5+2√6)=√(5+√24)
$\sqrt{5+ \sqrt{24} } = \sqrt{ \frac{5+ \sqrt{25-24} }{2} } + \sqrt{ \frac{5- \sqrt{25-24} }{2} }$
√(5+√24)=√3+√2

(√3-√2-√3-√2)²=(-2√2)²=8∈N