Question

Sa se calculeze media aritmetica si media geometrica a numerelor :
x ≈2√ 150 + 2√3 (3√12 -√50
y≈2√54{√216-√27(√72-√50)}
z≈√8supra3 · { 5√6-√8(√75-2√12)}

Answer 1

Media aritmetica este (x + y + z)/3 
x = 2√ 150 + 2√3 (3√12 -√50) = 2√150 + 6√36 -2√150 = 6 × 6 = 36

y = 2√54{√216-√27(√72-√50)} = 2√6×9 [ √9×4×6 - √9×3 (√9×8 - √25×2)] =
= 6√6 [ 6√6 - 3√3 (6√2 - 5√2)] = 6√6 (6√6 - 3√6) = 6√6 × 3√6 = 6 × 6 × 3 = 108

z = √8/3 · [5√6 - 2√2(5√3 - 4√3)] = 2√2/√3 × (5√6 - 2√6) = 2√2/√3 × 3√6 =
= 2 × 2 × 3 = 12

(x + y + z)/3 = (36 + 108 + 12)/3 = 156/3 = 52
Media geometrica: ∛xyz = ∛36×108×12 = ∛2²×3²× 3³ ×2² × 2² ×3 =
= ∛2^6 × 3^6 = 2² × 3² = 36