Question

Va rog din suflet!! ​

Answer 1

Răspuns:

x = - 4/5 ∈ Q

Explicație pas cu pas:

x = √1,25 : [(√(0,75/1,(6)) - 4/√5]³

√1,25 = √(125/100) = √(5³/10²) = 5√5/10 = √5/2

0,75 = 75/100⁽²⁵ = 3/4

1,(6) = (16-1)/9 = 15/9⁽³ = 5/3

3/4 : 5/3 = 3/4 ·3/5 = 9/20

√(0,75/1,(6)) = √(9/20) = 3/2 ·1/√5 = 3√5/(2·5) = 3√5/10

4/√5 = 4√5/5

x = √5/2 : (3√5/10 - ²⁾4√5/5)³

x = √5/2 :  (-5√5/10)³

x = √5/2 : (-√5/2)³ =>

x = √5/2 ·(-2³/5√5)

x = - 4/5 ∈ Q