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3. Prove that AABC is right-angled at A if AB 2n+1, AC 2+1) and BC -2n(n +1)+1. |
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Answer» if ABC is right angled at A then it must follow pythagoras theoremgiven AB=2n+1AC=2n(n+1)BC=2n (n+1)+1to prove AB^2 +AC^2 =BC^2LHS={2n+1}^2 +{2n (n+1)}^2=(4n^2 +1 +4n )+{4n^2 (n^2 +2n+1)}=4n^4 +8n^3 +8n^2+4n+1RHS={2n(n+1)+1}^2={4n^4 +8n^3 +4n^2 +1+4n^2 +4n}=4n^4 +8n^3 +8n^2 +4n+1we got LHS=RHS pythagoras theorem is satisfied so ABC is right angled at A |
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