a) m_g = √(x*y) = √[(√3+√2)(√7-√6)(√3-√2)(√7+√6)] =
= √[(√3+√2)(√3-√2)*(√7+√6)(√7-√6)]=
= √[(√3²-√2²)(√7²-√6²)] = √[(3-2)(7-6)] = √1 = 1
b) m_g = √(x*y) = √[(√5-√4)(√6+√5)(√7-√3)*(√5+√4)(√6-√5)(√7+√3)] =
= √[(√5-√4)(√5+√4)*(√6+√5)(√6-√5)*(√7-√3)(√7+√3)] =
= √[(√5²-√4²)*(√6²-√5²)*(√7²-√3²)] =
= √[(5-4)*(6-5)*(7-3)] =
= √(1*1*4) = 2
Atat la a), cat si la b), am aplicat (sub radicali) formula (a+b)(a-b) = a²-b², dar mai intai, am grupat parantezele pt. a vedea aceasta formula.
