[tex] \sqrt{a \times b} = 6 \sqrt{6} \: \: \: \: \: \: \: \: \: \:[/tex]
[tex]a \times b = (6 \sqrt{6} {)}^{2} = 36 \times 6 = 216[/tex]
[tex] \sqrt{b \times c} = 2 \sqrt{15} [/tex]
[tex]b \times c = {(2 \sqrt{15)} }^{2} = 4 \times 15 = 60[/tex]
[tex] \sqrt{a \times c} =3 \sqrt{10} [/tex]
[tex]a \times c = {(3 \sqrt{10)} }^{2} = 9 \times 10 = 90 [/tex]
a•b=216
b•c=60
a•c=90
a=216/b
c=60/b
a•c=216/b•60/b=12960/b^2=90
b^2=12960:90=144
[tex]b = \sqrt{144} = + 12 \: sau \: - 12[/tex]
deoarece b este pozitiv => b=12
a=18
c=5
