Question

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Ex. 2​

Answer 1

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

---------

1/2 < 1/√3

3/8 < 1/√5

5/16 < 1/√7

1/2 + 3/8 + 5/16 < 1/√3 + 1/√5 + 1/√7

Answer 2

Răspuns:

$\frac{ \sqrt{2} }{2} + \frac{ \sqrt{3} }{2} \geqslant \frac{7}{6}$

$\frac{ \sqrt{2} }{2} + \frac{ \sqrt{3} }{2} \\ este \: egal \: cu \: 1.28446$

$\frac{7}{6} \\ egal \: cu \: 1.16667$

$1.28446 \geqslant 1.16667$

Solutia este adevarata