Question

Se considera numerele reale $a= \frac{1}{ \sqrt{5}+2 } + \frac{1}{3+ \sqrt{8} }$ si [tex]b= \frac{1}{ \sqrt{5} -2} + \frac{1}{3- \sqrt{8} }
[/tex] . Aratati ca a+b=$6+2 \sqrt{5}$ .

Answer 1

a+b= {1 / (√5 + 2) + 1 / (√5 - 2) }  + {1 /(3 + √8) + 1 / (3 - √8)}
In fiecare paranteza acolada aducem la acelasi numitor

a + b = {(√5 - 2 + √5 - 2) / [(√5 + 2)(√5 - 2) ]} + {(3 - √8 + 3 + √8) / [(3 + √8)(3 - √8)] } =
={2√5 / [√5² - 2²] } / {6 / [3² - √8²]}   =  2√5 /1  +  6 / 1 =  6 + 2√5    cctd