Question

x=1/√2-1 + 1/√2+1 si y= √2·(√2+1/√2)
a) aratati ca x·(√8-√2)=4
b) Calculati : x la a 2-a - y
Dau 40 puncte !

Answer 1

x = ( √2 + 1) / ( √2 -1) ·(√2 +1) +  (√2 -1)  / ( √2 +1 )· (√2 -1) 
x = (√2 + 1) / [ √2² - 1² ] + (√2 -1)  / [√2² -1² ]
       √2² - 1² = 2 -1 =1 
x = √2 +1 + √2 -1 = 2√2 
x·(√8 - √2) = x·√2·(√4 - 1) = 2√2  ·√2 · ( 2 -1) = 2√4 ·1 = 2·2 = 4 
y = √2·(√4 + 1) / √2 = √4 + 1 = 2 +1 = 3 
x²  - y = (2√2)²  - 3 = 8 -3 = 5