Question

Calculați va rog repede

Answer 1

formula radicalilor compusi
a=√(3+√5)-√(3-√5)=√10/2+√2/2-√10/2+√2/2=√2
√(3+√5)=√[3+√(9-5)]/2+√[3-√(9-5)]/2=√(3+2)/2+√(3-2)/2=√5/2+√1/2=
=√10/2+√2/2
√(3-√5)=√[3+√(9-5)]/2-√[3-√(9-5)]/2=√(3+2)/2-√(3-2)/2=√5/2-√1/2=
=√10/2-√2/2

b=√(4-√7)-√(4+√7)=√14/2-√2/2-√14/2-√2/2=-√2
√(4-√7)=√[4+√(16-7)]/2-√[4-√(16-7)]/2=√(4+3)/2-√(4-3)/2=√7/2-√1/2=
=√14/2-√2/2
√(4+√7)=√[4+√(16-7)]/2+√[4-√(16-7)]/2=√(4+3)/2+√(4-3)/2=√7/2+√1/2=
=√14/2+√2/2

a²+b²=(√2)²+(-√2)²=2+2=4
a+b=√2+(-√2)=0