Răspuns
Explicație pas cu pas:
a / x = 3 ⇒ x / a = 1 / 3
x / a = y / b = z / c = 1 / 3
⇒ a = 3 x; b = 3 y si c = 3 z
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a) ( a + b + c ) / ( x + y + z ) = 3
= ( 3 x + 3 y + 3 z ) / ( x + y + z ) =
= 3 ( x + y + z ) / ( x + y + z ) =
= 3
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b) ( 2 a + 3 b + 4 c ) / ( 2 x + 3 y + 4 z ) = 3
= ( 2 × 3 x + 3 × 3 y + 4 × 3 z ) / ( 2 x + 3 y + 4 z ) =
= 3 ( 2 x + 3 y + 4 z ) / ( 2 x + 3 y + 4 z ) =
= 3
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c ) ( x² + y² + z² ) / ( a² + b² + c² ) = 1 / 9
= ( x² + y² + z² ) / ( 9 x² + 9 y² + 9 z² ) =
= ( x² + y² + z² ) / 9 ( x² + y² + z² ) =
= 1 / 9
