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Minh Flip Bottle
Jun 19, 2020

Problem 1, Vietnamese National Olympiad - 2002.

I've already solved it. Let's see if you can!

Solve the following equation:



0
1
Ian Fowler
Best Answer
  ·  Jun 19, 2020

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.

1
Ian Fowler
Jun 20, 2020

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.