<p>Find the number of real solutions of \([x]^2+2[x+2]-7=0\).</p>
Step-by-Step Solution
<div class="solution"><p>Use [x+2]=[x]+2. Let n=[x]: n^2+2n-3=0 \to n=1 or n=-3. Each gives an interval of solutions \to infinitely many.</p><div class="trap-box"><strong>Trap:</strong> Equation is in n=[x], not directly in x. Once solved, convert back to interval.<div class="key-concept"><strong>Key Concept:</strong> Floor equation \to [x]=n \to x\in[n,n+1)
Correct Answer: Infinitely many