Question

Aratati ca numarul $a = [ \sqrt{6} ( \frac{7}{ \sqrt{3} } - \frac{3}{ \sqrt{2} } ) + \sqrt{3(} 6- \frac{4 \sqrt{6} }{3} )]( \sqrt{3} - \sqrt{2} )$ este numar natural.

Answer 1

a=[7√2-3√3+6√3-$\frac{4 \sqrt{18} }{3}$](√3-√2)
a=(7√2+3√3-$\frac{4*3 \sqrt{2} }{3}$)(√3-√2)
a=(7√2+3√3-4√2)(√3-√2)
a=(3√2+3√3)(√3-√2)
a=3(√3+√2)(√3-√2)
a=3[(√3)²-(√2)²]=3(3-2)=3*1=3