Question

Dau coroană
Va rog frumos
​

Answer 1

Răspuns:

Explicație pas cu pas:

x o y = xy - 5x - 5y + 30

a) 5 o 2021 = 5·2021 - 5·5 - 5·2021 + 30 = -25+30 = 5 =>

5 o 2021 = 5

b) x o y = xy - 5x - 5y + 30 = xy - 5x - 5y + 25 + 5 =

= x(y-5) - 5(y-5) + 5 = (y-5)(x-5) + 5 = (x-5)(y-5) + 5

x o y =  (x-5)(y-5) + 5 ; (∀) x,y ∈ R

c) m² o n = 16 <=>

(m²-5)(n-5)+5 = 16 =>

(m²-5)(n-5) = 11 ; m,n ∈ Z =>

i) m²-5 = -1 ; n-5 = -11 => m² = 4 => m₁,₂ = ±2 ; n = -6

ii) m²-5 = -11 ; n-5 = -1  => m² = -6 => m₁,₂ ∉Z ; nu convine

iii) m²-5 = 1 ; n-5 = 11 => m² = 6 => m₁,₂ = ±√6 ∉ Z ; nu convine

iv) m²-5 = 11 ; n-5 = 1 => m² = 16 => m₁,₂ = ±4 ; n = 6