Question

Daca x supra y=3 supra 5 calculati: a) 2x+y supra 3y-2x; b) x+y supra y-x; c) 5x-y supra x+y
Dau coroana

Answer 1

Răspuns:

Explicație pas cu pas:

x / y = 3 / 5 =>   x = 3 y / 5

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a)   ( 2 x + y ) / ( 3 y - 2 x ) =

= ( 2 × 3 y / 5 + y ) / ( 3 y - 2 × 3 y / 5 ) =

= ( 6 y + 5 y ) / 5  : ( 15 y - 6 y ) / 5 =

= ( 11 y / 5 ) × ( 5 / 9 y ) =

= 11 / 9

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sau mai simplu :   x / y = 3 / 5 ⇒ x = 3   si y = 5

( 2 x + y ) / ( 3 y - 2 x ) = ( 2 × 3 + 5) / ( 3 × 5 - 2 ×3) = 11 / 9

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b)  ( x + y ) / ( y - x ) = ( 3 + 5 ) / ( 5 - 3 ) = 8 / 2 = 4

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c)   ( 5 x - y ) / ( x + y ) = ( 5 × 3 - 5 ) / ( 3 + 5 ) = 10 / 8 = 5 / 4

sau

y = 5 x / 3

( 5 x - 5 x / 3 ) / ( x + 5 x / 3 ) =

= ( 15 x - 5 x ) / 3 : ( 3 x + 5 x ) / 3 =

= ( 15 x / 3 ) × 3 / 8 x =

= 15 / 8 = → simplific cu 3

= 5 / 4