Răspuns:
4, 8, 10, 12
Explicație pas cu pas:
[tex]b = 2a[/tex]
[tex]5b = 4c \iff5 \cdot 2a = 4c \\ \implies c = \frac{5a}{2} [/tex]
[tex]6c = 5d \iff \frac{6 \times 5a}{2} = 5d \\ \implies d = 3a[/tex]
[tex]{a}^{2} + {b}^{2} + {c}^{2} + {d}^{2} = 324 \\ {a}^{2} + {(2a)}^{2} + {\Big( \frac{5a}{2} \Big)}^{2} + {(3a)}^{2} = 324 \\ {a}^{2} + {4a}^{2} + \frac{{25a}^{2} }{4} + {9a}^{2} = 324 \\ 14 {a}^{2} + \frac{{25a}^{2} }{4} = 324 \iff 81 {a}^{2} = 1296 \\ [/tex]
[tex]{a}^{2} = 16 \implies \bf a = 4 \\ b = 2 \cdot 4 \implies \bf b = 8 \\ c = \frac{5 \cdot 4}{2} \implies \bf c = 10 \\ d = 3 \cdot 4 \implies \bf d = 12[/tex]
