Question

4 si 6
Va rooog

DAU COROANA

Answer 1

4.
b=(a-rad3)^100= [(a-rad3)^50]^2, este in mod evident patratul perfect al lui 
(a-rad3)^50, oricare ar fi a, nu numai pentru acel a dat.

6. Radicali multipli.
Formula: rad(a+/-radb) = rad(a+c  / 2) +/- rad(a-c / 2), unde c=rad(a^2 - b) si a,b,c∈N*(multimea numerelor naturale fara zero)

rad(9-4rad5): c=rad(81-16*5)=rad1=1
=rad(9+1 / 2) - rad(9-1 /2) = rad5-rad4 = rad5 - 2 (1)
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rad(12-6rad3): c=rad(144-36*3)=rad(144-108)=rad36=6
=rad(12+6 / 2) - rad(12-6 / 2) = 3 - rad3 (2)
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rad(8-2rad15): c=rad(64-60)=rad4=2
=rad(8+2 / 2) - rad(8-2 / 2) = rad5 -rad3 (3)
(1)+(2)-(3)= rad5-2+3-rad3-rad5+rad3= 1∈N.