👤

Buna... ma ajutati? Determinati numarul natural n care verifica egalitatile: a) n^2-3^2=4^2
b) n:(4^2)^2=1 c) 4^n+4^n-1=80


Răspuns :

a)

[tex] {n}^{2} - {3}^{2} = {4}^{2} [/tex]

<=> n^2 - 9 = 16

<=> n^2 = 16 + 9

<=> n^2 = 25

<=> n ∈ { - 5, 5 }

b)

[tex]n \div ({{4}^{2} })^{2} = 1[/tex]

<=> [tex]n \div {4}^{4} = 1[/tex]

<=> [tex]n = {4}^{4} [/tex]

----------ᵈⁱᵃ----------