Question

$\frac{a}{b} =7- 4\sqrt{3} atunci \frac{ a^{2} + b^{2} }{ ab } =?$

Answer 1

(a² +b²) / ab ⇔ a /b + b / a

a /b = 7-4√3
b/a = (a/b) ^ (-1) = (7-4√3)^ (-1) = 1 / (7-4√3)

revenim la ex :
a /b +b / a = 7-4√3 + 1 /( 7-4√3) = 7-4√3 + (7+4√3) / (49-48)=7-4√3+7+4√3=14