[tex] x^{2} -y^{2}=48 [/tex] ⇔ [tex](x-y)(x+y)=48[/tex]
Avem [tex]x-y=6[/tex] ⇒ [tex]x+y = \frac{48}{6} = 8[/tex]
3(x+y) = 3 · 8 = 24
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[tex] x^{2} + \sqrt{24} = ( \sqrt{2}+ \sqrt{3}) ^{2} [/tex]
[tex] x^{2} + \sqrt{24} = 5 + 2 \sqrt{6} \\ x^{2} =5+2 \sqrt{6} - \sqrt{24} \\ x^{2} =5+2 \sqrt{6} -2 \sqrt{6} \\ x^{2} = 5[/tex]
De aici rezultă că x ∈ {5, -5}
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[tex]a=2 \sqrt{32} -6=8 \sqrt{2} -6 \\ b=3 \sqrt{8} +10=6 \sqrt{2}+10 \\ m _{a} = \frac{a+b}{2} = \frac{8 \sqrt{2}-6+6 \sqrt{2}+10 }{2} = \frac{14 \sqrt{2}+4 }{2} = \frac{2(7 \sqrt{2}+2) }{2} = 7 \sqrt{2} +2[/tex]
