IMC 2009 Q5
5. The square of a positive number is twice as big as the cube of that number. What is the number?
- A 8
- B 4
- C 2
- D \(\dfrac{1}{2}\)
- E \(\dfrac{1}{4}\)
Intermediate Mathematical Challenge 2009, Question 5. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D \(\dfrac{1}{2}\)
Let the number be \(x\). Then \(x^2 = 2x^3\), that is \(x^2(1 - 2x) = 0\). So \(x = 0\) or \(x = \tfrac{1}{2}\). However, \(x\) is positive, so the only solution is \(x = \tfrac{1}{2}\).
Solution © UK Mathematics Trust, from the IMC 2009 solutions.