Question

Efectuati:
a) $\sqrt{22- 12 \sqrt{2} }$ + $\sqrt{17-12 \sqrt{2} } - \frac{2}{ \sqrt{2} }$

Answer 1

formula radicalilor compusi
√(a-√b) = √(a+c)/2-√(a-c)/2
√(a+√b) = √(a+c)/2+√(a-c)/2
unde c=√(a²-b)

√(22-12√2)=√(22-√288)=√(22+14)/2-√(22-14)/2=√18-√4=3√2-2
a=22
b=288
c=√22²-288=√484-288=√196=14

√(17-12√2)=√(17-√288)=√(17+1)/2-√(17-1)/2=√9-√8=3-2√2
a=17
b=288
c=√17²-288=√289-288=√1=1

2/√2=2√2/2=√2

exercitiul devine

3√2-2+3-2√2-√2=1