Rad(x)=radical din x
Nu stiu daca am intes bine, dar:
rad(x-5)+rad(10-x)=3
Mutam +rad(10-x) in dreapta cu semn schimbat si ridicam ambele parti la puterea a 2-a
rad(x-5)=3-rad(10-x) |^2
rad(x-5)^2=(3-rad(10-x))^2
In stanga simplificam ordinul radicalului cu puterea si in dreapta folosim (a-b)^2
x-5=9-6rad(10-x)+10-x
x-5=19-6rad(10-x)-x
Mutam -6rad(10-x) in stanga si x-5 in dreapta
6rad(10-x)=19-x-x+5
6rad(10-x)=24-2x |:2
3rad(10-x)=12-x |^2
9(10-x)=144-24x+x^2
Folosim distributivitatea in stanga
90-9x=144-24x+x^2
Mutam expresia din dreapta in partea stanga si egalam cu 0
90-9x-144+24x-x^2=0
-54+15x-x^2=0=> -x^2+15x-54=0 |*(-1)
x^2-15x+54=0
Avem o ecuatie de gradul 2
ax^2+bx+c=0
discriminant:b^2-4ac
d:(-15)^2-4*1*54
d:9
x1=-b+rad(d)/2a
x2=-b-rad(d)/2a
x1,x2=15+-rad(9)/2
x1,x2=15+-3/2
x1=15+3/2=>x1=9
x2=15-3/2=>x2=6
S={6,9}
