Question

Rezolvati ecuatia:
$\sqrt{x-1}+2 \sqrt{1- x^{2} } = \sqrt{x+3} -2$

Answer 1

Punem conditiile de existenta ale radicalilor
x-1≥0 ⇒ x≥1, x∈[1,+∞)
1-x²≥0 ⇒x²≤1 ⇒ -1≤ x ≤ 1 ⇒ x∈[-1,1]
x+3≥0 ⇒ x≥-3 ⇒ x∈[-3, +∞)
Intersectand intervalele rezulta x=1