Question

$\sqrt{9-4\sqrt2}- \sqrt{9+4 \sqrt{2} } =$
vreau si explicatie, nu doar raspuns

Answer 1

formula radicalilor compusi
√(a+√b)=√[a+√(a²-b)]/2+√[a-√(a²-b)]/2
√(a-√b)=√[a+√(a²-b)]/2-√[a-√(a²-b)]/2

√(9-4√2)=√(9-√32)=√[(9+√81-32)/2]-√[(9-√81-32)/2]=
=√[(9+√49)/2]-√[(9-√49)/2]=√[(9+7)/2]-√[(9-7)/2]=√8-√1=2√2-1

√(9+4√2)=√(9+√32)=√[(9+√81-32)/2]+√[(9-√81-32)/2]=
=√[(9+√49)/2]+√[(9-√49)/2]=√[(9+7)/2]+√[(9-7)/2]=√8+√1=2√2+1


√(9-4√2)-√(9+4√2)=2√2-1-2√2-1=-2