Question

Rezolva in multimea numerelor reale ecuatiile: a)
$\frac{x}{3} = \frac{27}{x}$
b)
$\frac{x}{12} = \frac{75}{x}$
c)
$\frac{ - 18}{x} = \frac{ - x}{98}$
d)
$\frac{24}{ - x} = \frac{ - x}{54}$
e)
$\frac{2x}{9} = \frac{50}{x}$
f)
$\frac{2x}{45} = \frac{18}{5x}$
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Answer 1

Fie egalitatea raportelor a/b = c/d. Produsul mezilor este egal cu produsul extremilor axd = bxc

a) x² = 3*27

x² = 81

x = V81

x = ± 9

b) x² = 12*75

x² = 900

x = V900

x = ± 30

c) -x² = -1764

x² = 1764

x = V1764

x = ± 42

d) x² = 1296

x = V1296

x = ± 36

e) 2x² = 450

x² = 450/2

x² = 225

x = V225

x = ± 15

f) 10x² = 810

x² = 810/10

x = V81

x = ± 9