Răspuns:
a) +6; b) +20; c) +√30
Explicație pas cu pas:
a)
[tex]\frac{x}{12} = \frac{3}{x} \iff {x}^{2} = 12 \cdot 3 \\ {x}^{2} = 36 \iff {x}^{2} = {6}^{2} \\ x \pm 6 \implies \bf x = 6[/tex]
b)
[tex]\frac{16}{x} = \frac{x}{25} \iff {x}^{2} = 16 \cdot 25 \\ {x}^{2} = {4}^{2} \cdot {5}^{2} \iff {x}^{2} = {20}^{2} \\x \pm 20 \implies \bf x = 20[/tex]
c)
[tex]\frac{x}{2 \sqrt{5} } = \frac{ \sqrt{45} }{x} \iff {x}^{2} = 2 \sqrt{5} \cdot \sqrt{45} \\ {x}^{2} = {x}^{2} = 2 \sqrt{5} \cdot 3\sqrt{5} \iff {x}^{2} = 30 \\x \pm \sqrt{30} \implies \bf x = \sqrt{30} [/tex]
