Question

Вычислите :
(√(7+√13) - √(7-√13))²

Answer 1

$( sqrt{7+ sqrt{13} } - sqrt{7- sqrt{13} })^2= \ =( sqrt{7+ sqrt{13} })^2 - 2sqrt{7+ sqrt{13}}sqrt{7- sqrt{13}}+(sqrt{7- sqrt{13} })^2= \ =7+ sqrt{13} -2 sqrt{(7+ sqrt{13})(7- sqrt{13})} +7- sqrt{13} = \ =14-2 sqrt{7^2-( sqrt{13})^2 } =14-2 sqrt{49-13}=14-2 sqrt{36} = \ =14-2 sqrt{6^2}=14-2*6=14-12=2$