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Diophantus of Alexandria Born about 200AD Died about 284 AD Sometimes called ‘the father of algebra’ , he was the author of a series of books called ‘Arithmetica’. Although most of his work is now lost his texts dealt with solving algebraic equations which included the proof that the quadratic formula could solve any real quadratic equation. Algebraic Proof Monday 12th November 2014 Mathematical Proof In order to prove that a conjecture is true for all values we must use algebra. Here are a couple of useful things that you need to know: Here are a couple of useful things that you need to know: An algebraic expression to represent an even number is: An algebraic expression to represent an odd number is: In algebra we write consecutive numbers like this: In algebra we write consecutive even numbers like this: In algebra we write consecutive odd numbers like this: Here are a couple of useful things that you need to know: Even + Even = Even + Odd = Odd + Odd= Even × Even = Even × Odd = Odd × Odd = Mathematical Skills that you must be confident with are: • Simplifying algebraic expressions • Expanding brackets • Factorising • Solving Equations Show that: 2 2 2 (2n-1) + (2n+1) = 8n + 2 We need to manipulate the algebra on the LHS to show that is equal to the RHS Hence prove that the sum of the two squares of any two consecutive odd numbers is even. Matching Activity Can you sequence the proofs that you have been given? Each of you has two proofs you need to sort them into two separate proofs and glue them down to a sheet of A4 with a title. Proving the Quadratic Formula RAG 123 RAG your learning so far, then log into the blog. Pick the appropriate task for you.