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UKMT Mathematical Olympiad for Girls, 2013

Algebra Difficulty 3.0 AMC 10/12 Prove it United Kingdom

Find an integer solution of the equation $x^3 + 6x - 20 = 0$ and prove that the equation has no other real solutions.

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.