MathDB

3

Part of 1989 Federal Competition For Advanced Students

Problems(1)

real roots

Source: Austria 1989

7/10/2009
Let a a be a real number. Prove that if the equation x^2\minus{}ax\plus{}a\equal{}0 has two real roots x1 x_1 and x2 x_2, then: x_1^2\plus{}x_2^2 \ge 2(x_1\plus{}x_2).
inequalities proposedinequalities