a,b,c=?
[tex]ma = \frac{a + b + c}{3} = 4 + 8 \sqrt{2} [/tex]
=>
[tex]a + b + c = 12 + 24 \sqrt{2} [/tex]
a.
[tex]a = 3 + \sqrt{32} = 3 + 4 \sqrt{2} [/tex]
[tex]b = 5 + \sqrt{72} = 5 + 6 \sqrt{2} [/tex]
c=?
[tex]3 + 4 \sqrt{2} + 5 + 6 \sqrt{2} + c = 12 + 24 \sqrt{2} [/tex]
=>
[tex]c = - 8 - 10 \sqrt{2} + 12 + 24 \sqrt{2} [/tex]
[tex]c = 4 + 14 \sqrt{2} [/tex]
b.
[tex]2a = 3b = 6c[/tex]
=>
[tex]2a = 3b = > a = \frac{3b}{2} [/tex]
[tex]6c = 3b = > c = \frac{b}{2} [/tex]
[tex]a + b + c = 12 + 24 \sqrt{2} [/tex]
[tex] \frac{3b}{2} + \frac{b}{2} + \frac{2b}{2} = \frac{24}{2} + \frac{48 \sqrt{2} }{2} [/tex]
înmultim cu 2
[tex]6b = 24 + 48 \sqrt{2} [/tex]
[tex]b = \frac{24(1 + 2 \sqrt{2)} }{6} = 4 + 8 \sqrt{2} [/tex]
=>
[tex]a = \frac{3(4 + 8 \sqrt{2}) }{2} = 6 + 12 \sqrt{2} [/tex]
[tex]c = \frac{4 + 8 \sqrt{2} }{2} = 2 + 4 \sqrt{2} [/tex]
