Maths Olympiad Prep

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Problem 325

Algebra Difficulty 2.3 Find the answer CEMC Fermat

If x=1x=1 is a solution of the equation x2+ax+1=0x^{2} + ax + 1 = 0, what is the value of aa?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

Since x=1x=1 is a solution of the equation x2+ax+1=0x^{2} + ax + 1 = 0, then 12+a(1)+1=01^{2} + a(1) + 1 = 0 or 2+a=02 + a = 0 and so a=2a = -2.

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