Question

Determinati numerele intregi a si b pentru care a/(2-√3) + b/ (2+√3) = 6 -√3

Answer 1

a(2+√3)/1 + b(2-√3)/1 = 6 - √3
2a + a√3 + 2b - b√3 = 6 - √3
2(a+b) = 6    a+b = 3
(a-b)·√3 = √3  a-b = 1
2a = 4     a = 2  b = 1

Answer 2

[tex] \frac{2a+a \sqrt{3} }{4-3}+ \frac{2b-b \sqrt{3} }{4-3}=6- \sqrt{3} \\ 2a+2b+a \sqrt{3}-b \sqrt{3}=6- \sqrt{3} \\ 2(a+b)+ \sqrt{3}(a-b)=6- \sqrt{3} \\ \left \{ {{a+b=3} \atop {a-b=-1}} \right. 
Si rezolvi sistemul.