Question

Se cansidera nr reale
a=1-8/radical2 + radical98-12/radical18
b=radical96(1/radical12-1/radical48)-(radical6)⁰
Calculati media aritmetica si media geometrica ale nr reale a si b

Answer 1

Răspuns:

a = 1 - 8/√2 + √98 - 12/√18

= 1 - 8√2/2 + 7√2 - 12√18/18

= 1 - 4√2 + 7√2 - 2√2

= 1 + √2

b = √96(1/√12 - 1/√48) - (√6)⁰

= √96(1/2√3 - 1/4√3) - 1

= √96(2/4√3 - 1/4√3) - 1

= √96×1/4√3 - 1

= √32/4 - 1

= 4√2/4 - 1

= √2 - 1

Ma = (a + b)/2 = (1 + √2 + √2 - 1)/2 = 2√2/2 = √2

Mg = √a×b = √(√2 + 1)(√2 - 1) = √2 - 1 = √1 = 1