Question

radical x – 5+ radical 10 – x = 3​
va roggg, imi trebuie urgent!!!!

Answer 1

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}