Question

Daca S={-4;3} este multimea solutiilor ecuatiei x^2 +(m-n)x - (m+n+5)=0
avunci m=............................... si n=...............................
^ - la puerea

Answer 1

S={-4;3}⇒x=-4 sau x=3
(-4)↑2-4(m-n)-m-n-5=0
16-4m+4n-m-n-5=0
11-5m+3n=0
-5m+3n=-11
5m-3n=11
9+3(m-n)-m-n-5=0
9+3m-3n-m-n-5=0
9+2m-4n-5=0
4+2m-4n=0
2+m-2n=0
m-2n=-2
2n-m=2
$\left \{ {{5m-3n=11} \atop {2n-m=2}} \right. \left \{ {{5m-3n=11} \atop {-m+2n=2}} \right. \left \{ {{5m-3n=11} \atop {-5m+10n=10}} \right.$⇒7n=21⇒n=3⇔m=4