Question

3($\sqrt{x+2} +2)=x+8$ ...nu stie nimeni?:)

Answer 1

[tex] \sqrt{x+2} =x+8-2\\ \sqrt{x+2} =x+6(1)\\[/tex]
Conditiile de existenta:
x+2≥0=>x≥-2
x+6≥0=>x≥-6
Din cele doua conditii, deducem ca x≥-2.
Ridicam egalitatea (1) la patrat in ambii membri:
x+2=(x+6)²
(x+6)²=x+2
x²+12x+36=x+2
x²+11x+34=0
Δ=11²-4·34
Δ=121-136<0
Deducem ca ecuatia nu admite solutii reale.