Question

$Sa~se~rezolve: \\ \\ A=\{x\in R|x= \sqrt[4]{ \frac{16-3n}{4}},n\in N } \}~Intersectat~cu~(R/Q)$

Answer 1

pt ca radicalul de ordin parsa existe
16-3n≥0
16/3≥n
n≤16/3 si n∈N
deci n∈{0;1;2;3;4;5}

pt n=0
√√4=√2∈R\Q

pt n=1, x=√√(13/4)∈R\Q
n=2 , x=√√(5/2)∈R\Q
n=3, x=√√(7/4) ∈R\Q
n=4, x=√√1=1∈N⊂Q
n=5, x=√√(1/4)=1/√2=√2/2 ∈R\Q


A∩ (R\Q)={√√(13/4);√√(5/2);√√(7/4);√2/2;√2 }
am folosit notatia√√ pt radicalde ordinul 4

Answer 2

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