Question

Cat de repede puteți va rog!!!​

Answer 1

Răspuns:

Explicație pas cu pas:

a) x = 19·9 + 19·10 = 19·(9+10) = 19·19 = 19² = patrat perfect

√x = √(19²) = 19

b) x = 2¹¹-2¹⁰ = 2¹⁰·(2-1) = 2¹⁰ = 2⁵ˣ² = (2⁵)² = patrat perfect

√x = √[(2⁵)²] = 2⁵ = 32

c) x = 200+199·200 = 200·(1+199) = 200·200 = 200² =  patrat perfect

√x = √(200²) = 200

d) x = n+n·(n-1) = n·(1+n-1) = n·n = n² = patrat perfect , n ∈N*

√x = √(n²) = n

e) x = √441 + √[(42·43+43·44)/2] =

= 21 + √[43·(42+44)/2] =

= 21+√(43·86/2) =

= 21+√(43·43) =

= 21+√(43²) =

= 21+43 = 64 = 8² = patrat perfect

√x = √64 = 8

f) x = [(3ⁿ⁺²-3ⁿ⁺¹-2·3ⁿ)/3ⁿ] ; n ∈ N

x = [3ⁿ·(3²-3-2)/3ⁿ]

x = 9-5 = 4 = 2² =  patrat perfect

√x = √2² = 2