Răspuns:
Explicație pas cu pas:
a)
1/√2 + 1/√3 = √2/2 + √3/3 = 3√2/6 + 2√3/6 = (3√2 + 2√3)/6
1 1/6 = 7/6
(3√2 + 2√3)/6 ≥ 7/6
3√2 + 2√3 ≥ 7
ridicam la patrat
18 + 12√6 + 12 ≥ 49
30 + 12√6 ≥ 49
12√6 ≥ 49 - 30
12√6 ≥ 19
ridicam la patrat
864 ≥ 361 adevarat
____________________
b)
1/2 + 3/8 + 15/48 = 1/2 + 3/8 + 5/16
1/2 < 1/√3 ridicam la patrat
1/4 < 1/3 adevarat
3/8 < 1/√5 ridicam la patrat
9/64 < 1/5
9*5 < 64
45 < 64 adevarat
5/16 < 1/√7 ridicam la patrat
25/256 < 1/7
25*7 < 256
175 < 256 adevarat
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1/2 < 1/√3
3/8 < 1/√5
5/16 < 1/√7
1/2 + 3/8 + 5/16 < 1/√3 + 1/√5 + 1/√7
