Question

a)√x-1+√x+3=2
b)√2x-1+√2-x=2

Answer 1

Răspuns

Explicație pas cu pas:

a) Conditii existenta: x-1>0,x>1

x+3>0,x>-3

Ridici la patrat toata ecuatia: (x-1)+2(x-1)(x+3)+x+3=4

x-1+2(x^2+3x-x-3)+x+3=4

x-1+2x^2+6x-2x-6+x+3-4=0

2x^2+6x-8=0  

Imparti la 2 toata ecuatia : x^2+3x-4=0

∆= b^2-4ac = 9+16 = 25, √∆=5

x1=(-b+√∆)/2a = (-3+5)/2=1

x2=(-b-√∆)/2a = (-3-5)/2=-4

Deci multimea solutiilor S={1}

Si la b) faci cam la fel :))