Problem 1, Vietnamese National Olympiad - 2002.

Question

I've already solved it. Let's see if you can! Solve the following equation:

Ian Fowler · Accepted Answer

you're right. I knew 3 was it before I started. the 10-3x was a give-away. but there could have been others so I went for it. These types of equations are usually fudged so they have an integer solution. Thanks.

Ian Fowler · Answer

Square both sides and the 4's will subtract out. Square both sides again and you get a quartic . Solve by inspection to get x = 3 or x = -2 Use long division You will get 2 linear and 1 quadratic factor The quadratic has no real roots Test the 3 and -2 in the original - only 3 works.

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