Question

a supra b=0,(6), atunci 3a+15b supra 12a-2b este egal cu?

Answer 1

Răspuns:

Explicație pas cu pas:

a / b = 0,(6) = 6 / 9 = 2 / 3

a / b = 2 / 3 =>    a = 2   si b = 3

( 3 a + 15 b ) / ( 12 a - 2 b ) = 17 / 6

= ( 3 × 2 + 15 × 3 ) : ( 12 × 2 - 2 × 3 ) =

= ( 6 + 45 ) : ( 24 - 6 ) =

= 51 / 18 =  → simplific cu 3

= 17 / 6 =

= 2,8(3)

_____________________

sau:

⇒  3 a = 2 b ⇒   b = 3 a / 2

_______________________

( 3 a + 15 b ) / ( 12 a - 2 b ) = 17 / 6 = 2,8(3)

= 3 × ( a + 5 b ) / 2 × ( 6 a - b ) =

= 3 × ( a + 5 × 3 a / 2 ) /  2 × ( 6 a - 3 a / 2 ) =

= 3 × ( 2 a / 2+ 15 a / 2) : [ 2 × ( 12 a / 2 - 3 a / 2 ) ] =

= 3 × ( 17 a / 2 ) : ( 2 × 9 a / 2 ) =

= ( 51 a / 2 ) : 9 a =

= ( 51 a / 2 ) × 1 / 9 a =

= 17 / ( 2 x 3 ) =

= 17 / 6