WAEC Mathematics 2018 Theory — Question 20

Question 20 of 23 from the West African Examinations Council (WAEC) Mathematics 2018 Theory paper, with the correct answer and a full explanation.

12.(b) Using the method of completing the square, solve: (1−x)/x + x/(1−x) = 5/2

Model answer

Let u = x/(1−x); then 1/u + u = 5/2 → 2u²−5u+2=0 → u=2 or u=½. Solving x/(1−x)=2 gives x=2/3; solving x/(1−x)=½ gives x=1/3. So x = 1/3 or 2/3.

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