Question

Va rog mult ! Daca a/x =3 si x/a=y/b=z/c atunci calculeaza:
a)a+b+c/x+y+z.
b)2a+3b+4c/2x+3y+4z
c)x la puterea 2+y la puterea 2+z la puterea 2/a la puterea 2+b la puterea 2+c la puterea 2.

Answer 1

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