<p>Find the number of real solutions of <span class="math-inline">\([x]^2+2[x+2]-7=0\)</span>.</p>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>Use [x+2]=[x]+2. Let n=[x]: n²+2n-3=0 → n=1 or n=-3. Each gives an interval of solutions → 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><div class="key-concept"><strong>Key Concept:</strong> Floor equation → [x]=n → x∈[n,n+1)</div></div>
Correct Answer: Infinitely many