( x +y) · ( x² + xy + y² ) =126 / :5
↓ =5
x² + xy + y² = 126 /5
( x +y ) ² - x y = 126 /5 ; 25 - xy = 126/5 ; 25 - 126/5 = xy
5² xy = - 1/5
suma necunosc. = 5 si prod = - 1/5
sistemul este simetric , formam ec. gr. II t² - S·t + P =0
t² - 5t - 1/5 =0 ; 5t² - 25t - 1 =0 ; Δ = 625 +20 = 645
t₁ = ( 25 - √645 ) /10 si t₂ = ( 25 + √645 ) /10
sistemul simetric daca are solutia ( a , b) atunci si ( b , a ) este solutie
Sol = { ( 25 - √645 ) /10; ( 25 +√645 ) /10) }U { ( 25+√645 ) /10 ; ( 25 -√645) /10 }
