Question

Вычислите:
$sqrt{14+6sqrt{5}}-sqrt{9-4sqrt{5}}$

Answer 1

$sqrt{14+6sqrt{5}}-sqrt{9-4sqrt{5}} = sqrt{9+6sqrt{5}+5}-sqrt{4-4sqrt{5}+5} = \ =sqrt{3^2+2cdot 3cdotsqrt{5}+( sqrt{5} )^2}-sqrt{2^2-2cdot2cdotsqrt{5}+( sqrt{5} )^2} = \ =sqrt{(3+ sqrt{5} )^2}-sqrt{(2- sqrt{5} )^2} =|3+ sqrt{5} |-|2- sqrt{5}|= \ =3+ sqrt{5} -(-(2- sqrt{5}))=3+ sqrt{5} +2- sqrt{5}=5$

Answer 2

14+6√5=9+5+6√5=3^2+2*3*√5+5=(3+√5)^2
9-4√5=2^2+5-2*2*√5=(√5-2)^2
В итоге 3+√5-(√5-2)=3+2=5