Three Compact Methods, Side by Side
One problem solved three short, distinct ways with a verified answer.
Works on any free AI · Best tool: Any AI chat (ChatGPT/Gemini/Claude/Copilot)
✅ How to use this effectively
- 1. Copy the prompt into any AI chat.
- 2. Replace the bracket parts with your details.
- 3. Paste your exact question where shown.
- 4. Send and read the three methods.
- 5. Pick the one your class will follow best.
🔧 If it is not right, reply with this: If two methods look the same, reply: 'Method 2 and 3 are too similar - replace one with a genuinely different approach and re-verify the final answer.'
THE PROMPT
ROLE: Act as a master mathematics teacher who explains the same problem in several short, distinct ways.
CONTEXT: This is for a [CLASS/GRADE] student preparing for [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. The teacher wants three COMPACT, genuinely different solution routes to one problem so students can choose the route that suits them.
YOUR TASK:
1. Read the question below and identify the single correct final answer.
2. Produce exactly THREE different methods to reach it. Each method must use a genuinely different idea (for example: direct formula, substitution, factoring, comparison, working backwards). Do not repeat the same idea twice.
3. Keep each method short - aim for 4 to 7 lines of working, no padding.
4. Number the steps inside each method.
INPUT: Here is the question: [PASTE THE QUESTION HERE]
HOW TO WORK IT OUT: Solve the problem fully in your own reasoning first and lock the correct final answer. Then write the three methods so that all three land on that SAME answer. Verify the final answer by at least two independent checks (for example, substitute the answer back, or use a different method's result as a cross-check). Never invent formulas or values; if a standard formula is used, state it plainly. Keep all mathematics fully legible using clean LaTeX or clear plain text (write fractions, powers and roots clearly).
OUTPUT FORMAT (use these exact headings, in this order):
PROBLEM RESTATED (one line)
FINAL ANSWER (state it once, up front, boxed in words like: Answer = ...)
METHOD 1 - <short name> (numbered steps)
METHOD 2 - <short name> (numbered steps)
METHOD 3 - <short name> (numbered steps)
VERIFICATION (show the two independent checks and confirm all methods agree)
ONE-LINE TIP (which method is fastest for an exam)
RULES: All three methods must reach the identical final answer. If they do not agree, stop, find the slip, and fix it before presenting. No skipped algebra in a way a student cannot follow. No decimal answers unless the question asks for decimals; keep exact values (fractions, surds) 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):
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🔗 Free tools & to reach me: https://jee-prompt-studio.pages.dev/
Questions, feedback or appreciation are always welcome.
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