Crack It With a Clever Substitution
The standard solution plus a substitution that collapses the problem.
Works on any free AI · Best tool: Any AI chat (ChatGPT/Gemini/Claude/Copilot)
✅ How to use this effectively
- 1. Paste the prompt into any AI chat.
- 2. Fill class and exam brackets.
- 3. Paste your question where shown.
- 4. Send and study the substitution chosen.
- 5. Note when that substitution generally helps.
🔧 If it is not right, reply with this: If the substitution feels random, reply: 'Explain in one line how a student would spot this substitution, then re-verify the answer.'
THE PROMPT
ROLE: Act as a mathematics teacher who shows the direct solution and a clever substitution that simplifies the same problem.
CONTEXT: For a [CLASS/GRADE] student in [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. Substitution is a powerful idea students often miss; the teacher wants to make the 'how did you see that?' moment explicit.
YOUR TASK:
1. Find the correct final answer to the question below.
2. DIRECT METHOD: solve it the usual way, numbered steps.
3. SUBSTITUTION METHOD: choose a smart substitution that makes the problem easier, state the substitution clearly, solve, then convert back to the original variable.
4. Explain in one plain line the SIGNAL in the problem that suggests this substitution, so students learn to spot it.
INPUT: Here is the question: [PASTE THE QUESTION HERE]
HOW TO WORK IT OUT: Solve privately and lock the correct answer. Both methods must reach it, and the substitution method must convert back to the original variable correctly. Verify with two independent checks. Never invent formulas; name any used. Keep all maths legible in clean LaTeX or plain text. State the substitution explicitly as 'Let ... = ...'.
OUTPUT FORMAT (exact order):
FINAL ANSWER (once)
DIRECT METHOD (numbered steps)
SUBSTITUTION METHOD (state 'Let ... = ...', numbered steps, then convert back)
HOW TO SPOT THIS SUBSTITUTION (one line)
VERIFICATION (two independent checks)
RULES: Both methods must give the identical answer. The substitution must genuinely simplify the work and be reversed correctly. Use exact values where possible.
MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.
CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.
GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.
SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
━━━━━━━━━━━━━━━━
🔗 Free tools & to reach me: https://jee-prompt-studio.pages.dev/
Questions, feedback or appreciation are always welcome.
━━━━━━━━━━━━━━━━