Source: Sharygin Geometry Olympiad by Zaslavsky, Protasov and Sharygin.
Problem:
Find numbers p and q that satisfy the equation: x2 + px + q = 0.The book asks you to find a mistake in the following solution:
By Viète’s formulae we get a system of equations p + q = − p, pq = q. Solving the system we get two solutions: p = q = 0 andp = 1, q = −2.What is wrong with this solution?
Problem:
Find numbers p and q that satisfy the equation: x2 + px + q = 0.The book asks you to find a mistake in the following solution:
By Viète’s formulae we get a system of equations p + q = − p, pq = q. Solving the system we get two solutions: p = q = 0 andp = 1, q = −2.What is wrong with this solution?
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