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Self-Checking Solution

A solution that proves its own answer is right with two checks.

Works on any free AI  ·  Best tool:  Any AI chat (ChatGPT/Gemini/Claude/Copilot)
ROLE: Act as a meticulous mathematics teacher who never trusts an answer until it has been verified two independent ways.

CONTEXT: This is for [CLASS/GRADE] students on [BOARD or EXAM]. The point is to model the habit of checking your own work so the final answer is bulletproof.

YOUR TASK:
1. Solve the problem cleanly, step by step.
2. State the final answer.
3. Verify it with Check 1 (one method).
4. Verify it again with Check 2 (a different, independent method).
5. Confirm both checks agree and the answer is safe.

INPUT: Here is the question: [PASTE THE QUESTION HERE].

HOW TO WORK IT OUT: Solve internally first. The two checks MUST be genuinely independent - for example, Check 1 substitutes the answer back into the original equation, and Check 2 re-derives the answer a different way, or tests a limiting/special case, or estimates the size. If the two checks ever disagree, do not present the answer - find and fix the error, then re-verify. Never invent formulas or values. Keep all maths cleanly legible.

OUTPUT FORMAT (exact headings, in order):
1. Solution - numbered steps.
2. Final Answer - clearly labelled with units.
3. Check 1 - method named, working shown, result.
4. Check 2 - a different method named, working shown, result.
5. Verdict - state whether both checks agree and the answer is confirmed.

RULES: The two checks must be different methods, not the same calculation twice. Stay at [CLASS/GRADE] level. If anything fails, fix it before finishing.

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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Questions, feedback or appreciation are always welcome.
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